a two unit general parallel system with n 2 cold standbys analytic and simulation approach abstract a parallel 2 n 2 system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the n 2 cold standbys we assume availability of n non identical non repairable units for replacement or support the system reliability is evaluated by recursive relations with unit lifetimes t i i 1 n that have a general joint distribution function f t on the basis of the derived expression simulation techniques have been developed for the evaluation of the system reliability and the mean time to failure useful when dealing with large systems or correlated unit lifetimes and less mathematically manageable distributions simulation results are presented for various lifetime distributions and comparisons are made with derived analytic results for some special distributions and moderate values of n

on uniqueness for the navier stokes system in 3d bounded lipschitz domains in this paper we prove uniqueness of solutions of the navier stokes system in cb 0 t l3 3 l 0 t l3 2 where is a bounded lipschitz domain in r3

quantitative inequality for the eigenvalue of a schrodinger operator in the ball abstract the aim of this article is to prove a quantitative inequality for the first eigenvalue of a schrodinger operator in the ball more precisely we optimize the first eigenvalue v of the operator l v v with dirichlet boundary conditions with respect to the potential v under l 1 and l constraints on v the solution has been known to be the characteristic function of a centered ball but this article aims at proving a sharp growth rate of the following form if v is a minimizer then v v c v v l 1 2 for some c 0 the proof relies on two notions of derivatives for shape optimization parametric derivatives and shape derivatives we use parametric derivatives to handle radial competitors and shape derivatives to deal with normal deformation of the ball a dichotomy is then established to extend the result to all other potentials we develop a new method to handle radial distributions and a comparison principle to handle second order shape derivatives at the ball finally we add some remarks regarding the coercivity norm of the second order shape derivative in this context

finite element error estimates for 3d exterior incompressible flow with nonzero velocity at infinity we consider a stationary incompressible navier stokes flow in a 3d exterior domain with nonzero velocity at infinity in order to approximate this flow we use the stabilized p1 p1 finite element method proposed by rebollo numer math 79 283 319 1998 following an approach by guirguis and gunzburger model math anal numer 21 445 464 1987 we apply this method to the navier stokes system with oseen term in a truncated exterior domain under a pointwise boundary condition on the artificial boundary this leads to a discrete problem whose solution approximates the exterior flow as is shown by error estimates

a mass transportation approach to quantitative isoperimetric inequalities a sharp quantitative version of the anisotropic isoperimetric inequality is established corresponding to a stability estimate for the wulff shape of a given surface tension energy this is achieved by exploiting mass transportation theory especially gromov s proof of the isoperimetric inequality and the brenier mccann theorem a sharp quantitative version of the brunn minkowski inequality for convex sets is proved as a corollary

reliability analysis of a two unit general parallel system with n 2 warm standbys abstract a parallel 2 n 2 system is investigated here where two units start their operation simultaneously and any one of them is replaced instantaneously upon its failure by one of the n 2 warm standbys we assume availability of n non identical non repairable units the unit lifetimes in full operational mode and in partial operational mode have general distribution functions g i and h i i 1 n respectively the system reliability is evaluated by recursive relations

the l p regularity problem on lipschitz domains this paper contains two results on the l p regularity problem on lipschitz domains for second order elliptic systems and 1 2 the solvability of the l p regularity problem is equivalent to a weak reverse holder condition with exponent p

stability of polya szegő inequality for log concave functions abstract a quantitative version of polya szeg inequality is proven for log concave functions in the case of steiner and schwarz rearrangements

the sharp quantitative isoperimetric inequality a quantitative sharp form of the classical isoperimetric inequality is proved thus giving a positive answer to a conjecture by hall

boundary value problems in morrey spaces for elliptic systems on lipschitz domains let q be a bounded lipschitz domain in rn n 3 let be a second order elliptic system with constant coefficients satisfying the legendre hadamard condition we consider the dirichlet problem u 0 in q u f on 4 where e 0 depends on q and 0 a 2 for n 3 we obtain existence and uniqueness results with nontangential maximal function estimate u 2 a q c f 2 a 0q if c satisfies the strong elliptic condition and 0 a min n 1 2 e we show that the neumann type problem u 0 in q g g 2 a dq on 9q vu wfp idci has a unique solution here h2 x dq is an atomic space with the property h2 x dq l2 a 9q the invertibility of layer potentials on l2 x dq and h2 x dq is also obtained finally we study the dirichlet problem for the biharmonic equation we establish a similar estimate in l2 x for the biharmonic equation in which case the range 0 a 2 is sharp for n 4 or 5

sharp dimension free quantitative estimates for the gaussian isoperimetric inequality we provide a full quantitative version of the gaussian isoperimetric inequality the difference between the gaussian perimeter of a given set and a half space with the same mass controls the gap between the norms of the corresponding barycenters in particular it controls the gaussian measure of the symmetric difference between the set and the half space oriented so to have the barycenter in the same direction of the set our estimate is independent of the dimension sharp on the decay rate with respect to the gap and with optimal dependence on the mass

free boundary regularity for almost minimizers abstract in this paper we study the free boundary regularity for almost minimizers of the functional j u u x 2 q 2 x u 0 x q 2 x u 0 x d x where q l almost minimizers satisfy a variational inequality but not a pde or a monotonicity formula the way minimizers do see 4 5 9 37 nevertheless using a novel argument which brings together tools from potential theory and geometric measure theory we succeed in proving that under a non degeneracy assumption on q the free boundary is uniformly rectifiable furthermore when q 0 and q is holder continuous we show that the free boundary is almost everywhere given as the graph of a c 1 function thus extending the results of 4 to almost minimizers

existence and geometric properties of solutions of a free boundary problem in potential theory let 0 g h l rn n 2 be two given density functions at least one of them bounded away from zero outside a compact set and g holder continuous we prove that for any compactly supported positive measure which is sufficiently concentrated e g has sufficiently high n 1 dimensional density there exists a bounded open set rn such that the newtonian potential of the measure hln ghn 1 agrees with that of outside some regularity of is obtained as well as several results on the geometry of example if h and g are constant then for any x the inward normal ray of at x if it exists intersects the closed convex hull of typeset by ams tex 1 2 bjorn gustafsson and henrik shahgholian

the quantitative faber krahn inequality for the robin laplacian abstract we prove a quantitative form of the faber krahn inequality for the first eigenvalue of the laplace operator with robin boundary conditions the asymmetry term involves the square power of the fraenkel asymmetry multiplied by a constant depending on the robin parameter the dimension of the space and the measure of the set

orderings of coherent systems with randomized dependent components abstract consider a general coherent system with independent or dependent components and assume that the components are randomly chosen from two different stocks with the components of the first stock having better reliability than the others then here we provide sufficient conditions on the component s lifetimes and on the random numbers of components chosen from the two stocks in order to improve the reliability of the whole system according to different stochastic orders we also discuss several examples in which such conditions are satisfied and an application to the study of the optimal random allocation of components in series and parallel systems as a novelty our study includes the case of coherent systems with dependent components by using basic mathematical tools and copula theory

resolvent estimates in l p for the stokes operator in lipschitz domains we establish the l p resolvent estimates for the stokes operator in lipschitz domains in mathbb r d d geqq 3 for frac 1 p frac 1 2 frac 1 2d varepsilon the result implies that the stokes operator in a three dimensional lipschitz domain generates a bounded analytic semigroup in l p for 3 2 e p 3 e this gives an affirmative answer to a conjecture of m taylor progr nonlinear differential equations appl vol 42 pp 320 334

faber krahn inequalities in sharp quantitative form the classical faber krahn inequality asserts that balls uniquely minimize the first eigenvalue of the dirichlet laplacian among sets with given volume in this paper we prove a sharp quantitative enhancement of this result thus confirming a conjecture by nadirashvili and bhattacharya weitsman more generally the result applies to every optimal poincare sobolev constant for the embeddings w 1 2 0 omega hookrightarrow l q omega

order statistics of dependent sequences consisting of two different sets of exchangeable variables we consider two different sets of exchangeable samples which are assumed to be dependent a single set of observations is obtained from these two dependent samples the distribution of single order statistic and the joint distribution of the minimum and an arbitrary order statistic are derived the results are illustrated in the context of reliability problem

spectral optimization for the stekloff laplacian the stability issue abstract we consider the problem of minimizing the first non trivial stekloff eigenvalue of the laplacian among sets with given measure we prove that the brock weinstock inequality asserting that optimal shapes for this spectral optimization problem are balls can be improved by means of a sharp quantitative stability estimate this result is based on the analysis of a certain class of weighted isoperimetric inequalities already proved in betta et al 1999 2 we provide some new sharp quantitative versions of these achieved by means of a suitable calibration technique

a factorization theorem for operators occurring in the stokes brinkman and oseen equations in many physical problems one is faced with solving partial differential equations of the form l 1 l 1 l 2 u 0 where l1 and l2 are linear operators it is found in many cases that the solution u is of the form u 1 u 2 where l 1 u 1 0 and l 1 l 2 u 2 0 in this paper we present sufficient conditions under which such a splitting is possible moreover we give explicit formulae for u1 and u2 for a given u we also show in some examples where the operators satisfy the sufficient conditions and such a splitting is used extensively in particular we find a class of solutions for the unsteady brinkman and unsteady oseen equations using the splitting that we propose

the dirichlet problem in non smooth domains dirichlet problem for an elliptic operator 2s laj jaj with smooth coefficients aij in domains d in rm m 3 with non smooth boundaries the domains we treat are given locally in some cm coordinate system by the graph of a continuous function qs with vq5 e li for some p 1 p oo such domains are called li domains see section 1 for the precise definitions note that l domains are usually called lipschitz domains if d is an li domain and x e d we study the elliptic measure a7 associated with s and d at x thus for f a continuous function on ad the formula u x hf x f doh gives the perron wiener brelot generalized soluid

an optimization problem with volume constraint we consider the optimization problem of minimizing dirichlet integral int omega nabla u 2 with volume constraint on the set u 0 we use a penalization method which for small values of the penalization parameter leads to a solution of the original problem

existence and uniqueness for a semilinear elliptic problem on lipschitz domains in riemannian manifolds ii abstract for a general class of semilinear equations in a lipschitz domain where m is a smooth compact riemannian manifold we establish the existence and uniqueness of solutions to dirichlet and neumann boundary problems the main contribution of this paper is that we consider rough boundary data that are typically just functions results of this type for the linear equation are typically obtained using singular integral techniques

interval reliability of typical systems with partially known probabilities abstract most probabilistic methods of the system reliability analysis assume that the component lifetime distributions are known precisely and the system components are independent the paper considers reliability analysis of typical systems when the above assumptions are violated and there is only some partial information about the component lifetime distributions the analysis is based on considering sets of possible probability distributions consistent with available information all resulting expressions are obtained in the explicit form the impact of incompleteness of initial data on the resulting system reliability measures is illustrated by a numerical example

commutator estimates for the dirichlet to neumann map of stokes systems in lipschitz domains abstract in the paper we establish commutator estimates for the dirichlet to neumann map of stokes systems in lipschitz domains the approach is based on dahlberg s bilinear estimates and the results may be regarded as an extension of 8 21 to stokes systems

a finite element method for 3d exterior oseen flows error estimates stationary oseen flows in a 3d exterior domain are discretized by applying a p1 p1 stabilized finite element method to the oseen system in a truncated exterior domain with an implicit pointwise artificial boundary condition on the truncating boundary error estimates are proved for this discretization the paper extends an approach which was introduced by guirguis and gunzburger rairo model math anal numer 21 1987 pp 445 464 for exterior stokes flows the stabilized p1 p1 method in question was introduced by rebollo numer math 79 1998 pp 283 319

weighted lq estimates for stationary stokes system with partially bmo coefficients abstract we prove the unique solvability of solutions in sobolev spaces to the stationary stokes system on a bounded reifenberg flat domain when the coefficients are partially bmo functions i e locally they are merely measurable in one direction and have small mean oscillations in the other directions using this result we establish the unique solvability in muckenhoupt type weighted sobolev spaces for the system with partially bmo coefficients on a reifenberg flat domain we also present weighted a priori l q estimates for the system when the domain is the whole euclidean space or a half space

integral equation methods for unsteady stokes flow in two dimensions we present an integral equation formulation for the unsteady stokes equations in two dimensions this problem is of interest in its own right as a model for slow viscous flow but perhaps more importantly as an ingredient in the solution of the full incompressible navier stokes equations using the unsteady green s function the velocity evolves analytically as a divergence free vector field this avoids the need for either the solution of coupled field equations as in fully implicit pde based marching schemes or the projection of the velocity field onto a divergence free field at each time step as in operator splitting methods in addition to discussing the analytic properties of the operators that arise in the integral formulation we describe a family of high order accurate numerical schemes and illustrate their performance with several examples

stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components abstract in this paper we compare the residual lifetime of a used coherent system of age t 0 with the lifetime of the similar coherent system made up of used components of age t here similar means that the system has the same structure and the component lifetimes have the same dependence joint reliability copula some comparison results are obtained for the likelihood ratio order failure rate order reversed failure rate order and the usual stochastic order similar results are reported for comparing inactivity time of a coherent system with lifetime of similar coherent system having component lifetimes same as inactivity times of failed components

reliability of coherent systems with a single cold standby component in this paper the influence of a cold standby component on a coherent system is studied a method for computing the system reliability of coherent systems with a cold standby component based on signature is presented numerical examples are presented reliability and mean time to failure of different systems are computed

a deteriorating cold standby repairable system with priority in use abstract in this paper a cold standby repairable system consisting of two dissimilar components and one repairman is studied in this system it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use after repair component 2 is as good as new while component 1 follows a geometric process repair under these assumptions using the geometric process and a supplementary variable technique some important reliability indices such as the system availability reliability mean time to first failure mttff rate of occurrence of failure rocof and the idle probability of the repairman are derived a numerical example for the system reliability r t is given and it is considered that a repair replacement policy based on the working age t of component 1 under which the system is replaced when the working age of component 1 reaches t our problem is to determine an optimal policy t such that the long run average cost per unit time of the system is minimized the explicit expression for the long run average cost per unit time of the system is evaluated and the corresponding optimal replacement policy t can be found analytically or numerically another numerical example for replacement model is also given

maximum modulus estimate for the solution of the stokes equations abstract a maximum modulus estimate for the nonstationary stokes equations in c 2 domain is found the singular part and regular part of poisson kernel are analyzed the singular part consists of the gradient of single layer potential and the gradient of composite potential defined on only normal component of the boundary data furthermore the normal velocity near the boundary is bounded if the boundary data is bounded if the normal component of the boundary data is dini continuous and the tangential component of the boundary data is bounded then the maximum modulus of velocity is bounded in whole domain

navier stokes equations on lipschitz domains in riemannian manifolds the navier stokes equations are a system of nonlinear evolution equations modeling the flow of a viscous incompressible fluid one ingredient in the analysis of this system is the stationary linear system known as the stokes system a boundary value problem bvp that will be described in detail in the next section layer potential methods in smoothly bounded domains in euclidean space have proven useful in the analysis of the stokes system starting with work of odqvist and lichtenstein and including work of solonnikov and many others see the discussion in chapter iii of 10 and in 17 for the case of flow in regions with smooth boundary a treatment based on the modern language of pseudodifferential operators can be found in 18 in 1988 e fabes c kenig and g verchota 6 extended this classical layer potential approach to cover lipschitz domains in euclidean space in 6 the main result concerning the constant coefficient stokes system on lipschitz domains with connected boundary in euclidean space is the treatment of the l dirichlet boundary value problem and its regular version to achieve this the authors solve certain auxiliary neumann type problems and then exploit the duality between these and the original bvp s at the level of boundary integral operators p deuring and w von wahl 4 made use of the analysis in 6 to demonstrate the short time existence of solutions to the navier stokes equations in bounded lipschitz domains in threedimensional euclidean space it was necessary in 4 to include the hypothesis that the boundary be connected the hypothesis that the boundary be connected pervaded much work on the application of layer potentials to analysis on lipschitz domains it was certainly natural to speculate that this restriction was an artifact of the methods used and not partly supported by nsf grant dms 9870018 partially supported by nsf grant dms 9877077 1991mathematics subject classification primary 35q30 76d05 35j25 secondary 42b20 45e05

stability in shape optimization with second variation we are interested in the question of stability in the eld of shape optimization precisely we prove that under structural assumptions on the hessian of the considered shape functions the necessary second order minimality conditions imply that the shape hessian is coercive for a given norm moreover under an additional continuity condition for the second order derivatives we derive precise optimality results in the class of regular perturbations of a domain these conditions are quite general and are satised for the volume the perimeter the torsional rigidity and the rst dirichlet eigenvalue of the laplace operator as an application we provide non trivial examples of inequalities obtained in this way

biased random walk conditioned on survival among bernoulli obstacles subcritical phase we consider a discrete time biased random walk conditioned to avoid bernoulli obstacles on mathbb z d d ge 2 up to time n this model is known to undergo a phase transition for a large bias the walk is ballistic whereas for a small bias it is sub ballistic we prove that in the sub ballistic phase the random walk is contained in a ball of radius o n 1 d 2 which is the same scale as for the unbiased case as an intermediate step we also prove large deviation principles for the endpoint distribution for the unbiased random walk at scales between n 1 d 2 and o n d d 2 these results improve and complement earlier work by sznitman ann sci ecole norm sup 4 28 3 345 370 371 390 1995

the method of layer potentials for the heat equation in lipschitz cylinders pour l equation de la chaleur dans des cylindres de lipschitz on etudie des problemes aux valeurs limites d initiales avec conditions de neumann et de dirichlet

on the lid driven problem in a porous cavity a theoretical and numerical approach the purpose of this paper is to analyze the motion of an incompressible viscous fluid through a porous medium located in a two dimensional square cavity i e the lid driven flow problem described by a generalized darcy brinkman model first we study the dirichlet boundary value problem for a generalized darcy brinkman system in a n dimensional bounded lipschitz domain n 2 3 when the given data belongs to some l 2 based sobolev spaces we obtain an existence and uniqueness result for this problem under the assumption of sufficiently small given data an existence and uniqueness result for the robin boundary value problem associated to the same nonlinear system is also formulated further we consider a special dirichlet boundary value problem for the generalized darcy brinkman system i e the lid driven problem associated with such a nonlinear system and we obtain the streamlines of the fluid flow for different reynolds and darcy numbers moreover we consider an additional sliding parameter that corresponds to a mixed dirichlet robin boundary value condition imposed on the upper moving wall and analyze the behavior of the flow with respect to such a parameter

the l p regularity problem for the stokes system on lipschitz domains we study the lp regularity problem for the stationary stokes system on lipschitz domains for any p 2 we show that a weak reverse holder inequality with exponent p is both necessary and sufficient for the solvability of the regularity problem with data in w1 p lnp we also obtain the w1 p estimate u lp q lp f lp in a bounded lipschitz domain rd for solutions to the dirichlet problem u q div f div u 0 in and u 0 on where 1p 12 12d e

boundary estimates in homogenization of systems of elasticity on lipschitz domains l p theory abstract the primary purpose of this paper is to investigate a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients arising in the theory of homogenization in lipschitz domains as a consequence for d 4 we prove that the l p neumann and l p dirichlet boundary value problems for systems of second order linear elasticity are uniquely solvable for 2 d 1 d 1 p 2 and 2 p 2 d 1 d 3 respectively

minimality via second variation for a nonlocal isoperimetric problem we discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts we show that critical configurations with positive second variation are local minimizers of the nonlocal area functional and in fact satisfy a quantitative isoperimetric inequality with respect to sets that are l 1 close the link with local minimizers for the diffuse interface ohta kawasaki energy is also discussed as a byproduct of the quantitative estimate we get new results concerning periodic local minimizers of the area functional and a proof via second variation of the sharp quantitative isoperimetric inequality in the standard euclidean case as a further application we address the global and local minimality of certain lamellar configurations

the lp boundary value problems on lipschitz domains abstract let be a bounded lipschitz domain in r n we develop a new approach to the invertibility on l p of the layer potentials associated with elliptic equations and systems in as a consequence for n 4 and 2 n 1 n 1 e p 2 where e 0 depends on we obtain the solvability of the l p neumann type boundary value problems for second order elliptic systems the analogous results for the biharmonic equation are also established

boundary integral approach for the mixed dirichlet robin boundary value problem for the nonlinear darcy forchheimer brinkman system abstract the purpose of this paper is to provide the solvability and uniqueness result to the mixed dirichlet robin boundary value problem for the nonlinear darcy forchheimer brinkman system in a bounded two dimensional lipschitz domain first we obtain a well posedness result for the linear brinkman system with dirichlet neumann boundary conditions by reducing the problem to the system of boundary integral equations based on the fundamental solution of the brinkman system and by analyzing this system employing a variational approach the result is extended afterwards to the poisson problem for the brinkman system and to dirichlet robin boundary conditions using the newtonian potential and the linearity of the solution operator further we study the nonlinear darcy forchheimer brinkman boundary value problem of dirichlet and robin type

the regularity of the stokes operator and the fujita kato approach to the navier stokes initial value problem in lipschitz domains abstract we study the regularity of the navier stokes equations in arbitrary lipschitz domains

nonparametric predictive reliability of series of voting systems abstract nonparametric predictive inference npi for system reliability reflects the dependence of reliabilities of similar components due to limited knowledge from testing npi has recently been presented for reliability of a single voting system consisting of multiple types of components the components are all assumed to play the same role within the system but with regard to their reliability components of different types are assumed to be independent the information from tests is available per type of component this paper presents npi for systems with subsystems in a series structure where all subsystems are voting systems and components of the same type can be in different subsystems as npi uses only few modelling assumptions system reliability is quantified by lower and upper probabilities reflecting the limited information in the test data the results are illustrated by examples which also illustrate important aspects of redundancy and diversity for system reliability

variable lorentz estimate for conormal derivative problems of stationary stokes system with partially bmo coefficients abstract we prove a global calderon zygmund type estimate in the framework of lorentz spaces for the variable power of the gradients to the solution pair u p of the conormal derivative problems of stationary stokes system it is mainly assumed that the leading coefficients are merely measurable in one of the spatial variables and have sufficiently small bounded mean oscillation seminorm in the other variables the boundary of domain belongs to the reifenberg flatness and the variable exponents p x satisfy the log holder continuity

localization for random walks among random obstacles in a single euclidean ball place an obstacle with probability 1 p independently at each vertex of mathbb z d and run a simple random walk before hitting one of the obstacles for d ge 2 and p strictly above the critical threshold for site percolation we condition on the environment where the origin is contained in an infinite connected component free of obstacles and we show that for environments with probability tending to one as n rightarrow infty there exists a unique discrete euclidean ball of volume d log 1 p n asymptotically such that the following holds conditioned on survival up to time n we have that at any time t in epsilon n n n for some epsilon n rightarrow n rightarrow infty 0 with probability tending to one the simple random walk is in this ball this work relies on and substantially improves a previous result of the authors on localization in a region of volume poly logarithmic in n for the same problem

on the mean residual life of a k out of n g system with a single cold standby component abstract the concept of mean residual life is one of the most important characteristics that has been widely used in dynamic reliability analysis it is a useful tool for investigating ageing properties of technical systems in this paper we define and study three different mean residual life functions for k out of n g system with a single cold standby component in particular we obtain explicit expressions for the corresponding functions using distributions of order statistics we also provide some stochastic ordering results associated with the lifetime of a system we illustrate the results for various lifetime distributions

layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains the symbolic calculus of pseudodifferential operators of mellin type is applied to study layer potentials on a plane domain q whose boundary 9q is a curvilinear polygon a singularity type is a zero of the determinant of the matrix of symbols of the mellin operators and can be used to calculate the bad values of p for which the system is not fredholm on lp 9q using the method of layer potentials we study the singularity types of the system of elastostatics lu uau au vdivu 0 in a plane domain q whose boundary 9k2 is a curvilinear polygon here u 0 and u a oo when a oo the system is the stokes system of hydrostatics for the traction double layer potential we show that all singularity types in the strip 0 re z i lie in the interval 1 1 so that the system of integral equations is a fredholm operator of index 0 on lp aq for all p 2 p oo the explicit dependence of the singularity types on a and the interior angles 0 of aq is calculated the singularity type of each corner is independent of a if the corner is nonconvex introduction recently there has been considerable interest in using layer potentials to solve lp boundary value problems for elliptic operators and systems on a lipschitz domain q in r for the systems of elastostatics dkv and hydrostatics fkv dahlberg fabes kenig and verchota have used rellich type identities to prove that the double layer potential integral equations yield a fredholm operator of index 0 on l 2 q for p 2 only limited information is available on the boundary integral equations for general lipschitz domains in rn the general problem of the notion of symbol on the boundary of a general lipschitz domain is still very much open in this paper we treat a very special case a curvilinear polygonal domain in r in this 2 dimensional case a precise symbolic calculus of pseudodifferential operators of mellin type is available we show that certain double layer boundary integral equations yield operators which for all p 2 p 00 are received by the editors december 14 1988 1980 mathematics subject classification 1985 revision primary 35j25 45e05 research partially supported by the italian cnr 1990 american mathematical society 0002 9947 90 1 00 25 per page

convergence rates and w1 p estimates in homogenization theory of stokes systems in lipschitz domains abstract concerned with the stokes systems with rapidly oscillating periodic coefficients we mainly extend the recent works in 19 20 to those in term of lipschitz domains the arguments employed here are quite different from theirs and the basic idea comes from 37 originally motivated by 23 27 33 we obtain an almost sharp o e ln r 0 e convergence rate in l 2 space and a sharp o e error estimate in l 2 d d 1 space by a little stronger assumption under the dimensional condition d 2 we also establish the optimal o e convergence rate on pressure terms in l 2 space then utilizing the convergence rates we can derive the w 1 p estimates uniformly down to microscopic scale e without any smoothness assumption on the coefficients where 1 p 1 2 1 2 d and is a positive constant independent of e combining the local estimates based upon vmo coefficients consequently leads to the uniform w 1 p estimates here the proofs do not rely on the well known compactness methods

l2 solvability of the dirichlet neumann and regularity problems for parabolic equations with time independent holder continuous coefficients we establish the l 2 solvability of dirichlet neumann and regularity problems for divergence form heat or diffusion equations with timeindependent holder continuous diffusion coefficients on bou

on the navier problem for the stationary navier stokes equations the navier problem is to find a solution of the steady state navier stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary if is exterior it is required that the velocity converges to an assigned constant vector u0 at infinity we prove that a solution exists in a bounded domain provided a l2 is less than a computable positive constant and is unique if a w1 2 2 s l2 is suitably small as far as exterior domains are concerned we show that a solution exists if a l2 a u0 n l2 is small

dynamic network reliability modeling under nonhomogeneous poisson processes abstract in this paper we consider a two state up and down network consisting of n links we study the d spectrum based dynamic reliability of the network under the assumption that the links are subject to failure according to a nonhomogeneous poisson process several mixture representations are provided for the reliability function of residual lifetime of used networks under different conditions on the status of the network or its links these representations enable us to explore the residual reliability of operating networks in terms of the reliability functions of residual lifetimes of upper record values the distribution function of inactivity time of a network is examined under the condition that the network has failed by inspection time t stochastic ordering properties of the residual lifetimes of networks under conditional d spectra are investigated several examples and graphs are also provided to illustrate the established results

a geometric process maintenance model with preventive repair abstract in this paper a geometric process maintenance model with preventive repair is studied a maintenance policy t n is applied by which the system will be repaired whenever it fails or its operating time reaches t whichever occurs first and the system will be replaced by a new and identical one following the n th failure the long run average cost per unit time is determined an optimal policy t n could be determined numerically or analytically for minimizing the average cost a new class of lifetime distribution which takes into account the effect of preventive repair is studied that is applied to determine the optimal policy t n

confinement of brownian motion among poissonian obstacles in ℝ d d 3 consider brownian motion among random obstacles obtained by translating a fixed compact nonpolar subset of d d 1 at the points of a poisson cloud of constant intensity v 0 assume that brownian motion is absorbed instantaneously upon entering the obstacle set in szn conf sznitman has shown that in d 2 conditionally on the event that the process does not enter the obstacle set up to time t the probability that brownian motion remains within distance t1 4 from its starting point is going to 1 as t goes to infinity we show that the same result holds true for d 3 with t1 4 replaced by t1 d 2 the proof is based on sznitmans refined method of enlargement of obstacles 10 as well as on a quantitative isoperimetric inequality due to hall 4

a posteriori error estimates of stabilized low order mixed finite elements for the stokes eigenvalue problem in this paper we obtain a priori and a posteriori error estimates for stabilized low order mixed finite element methods for the stokes eigenvalue problem we prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues we define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that up to higher order terms the estimator is equivalent to the energy norm of the error we also present some numerical tests which show the performance of the adaptive scheme

curvature driven flows a variational approach this paper introduces a new mathematical approach to the study of time evolutions of solids k t in n space whose boundaries move with velocity equal to the weighted mean curvature derived from the boundary surface energy phi partial k t these flat phi curvature flows are limits of sequences of solutions to variational problems in which a sum of surface and bulk energy is minimized the construction works equally well for smooth elliptic phi s for nondifferentiable crystalline phi s and for anything in between the flows agree with classical smooth flows when the data is smooth and elliptic in any dimension and coincide with motion by crystalline curvature for polyhedral curves in the plane

a selection principle for the sharp quantitative isoperimetric inequality we introduce a new variational method for the study of isoperimetric inequalities with quantitative terms the method is general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter two notable applications are presented first we give a new proof of the sharp quantitative isoperimetric inequality in mathbb r n second we positively answer a conjecture by hall concerning the best constant for the quantitative isoperimetric inequality in mathbb r 2 in the small asymmetry regime

a boundary multiplier fictitious domain method for the steady incompressible navier stokes equations we analyze the error of a fictitious domain method with boundary lagrange multiplier it is applied to solve a non homogeneous steady incompressible navier stokes problem in a domain with a multiply connected boundary the interior mesh in the fictitious domain and the boundary mesh are independent up to a mesh length ratio

fluctuations of principal eigenvalues and random scales we investigate the principal dirichlet eigenvalue of the laplacian with soft poissonian obstacles in large boxes of d 2 with the help of our recent version of the method of enlargement of obstacles 18 we derive quantitative confidence intervals for these eigenvalues we also provide less quantitative estimates which however point out the correct size of fluctuations and indicate a stiffness in their behavior in the two dimensional case we derive geometric controls which relate these eigenvalues to certain empty circular droplets our results also have natural applications to the study of the location of minima of certain intermittent random variational problems motivated by 13 17

the stationary navier stokes system in nonsmooth manifolds the poisson problem in lipschitz and c 1 domains we consider the linearized version of the stationary navier stokes equations on a subdomain of a smooth compact riemannian manifold m the emphasis is on regularity the boundary of is assumed to be only c1 and even lipschitz and the data are selected from appropriate sobolev besov scales our approach relies on the method of boundary integral equations suitably adapted to the variable coefficient setting we are considering here applications to the stationary nonlinear navier stokes equations in this context are also discussed

boundary korn inequality and neumann problems in homogenization of systems of elasticity this paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients arising in the theory of homogenization we establish uniform optimal regularity estimates for solutions of neumann problems in a bounded lipschitz domain with l2 boundary data the proof relies on a boundary korn inequality for solutions of systems of linear elasticity and uses a large scale rellich estimate obtained in shen anal pde arxiv 1505 00694v2

estimates for green functions of stokes systems in two dimensional domains abstract we prove the existence and pointwise bounds of the green functions for stationary stokes systems with measurable coefficients in two dimensional domains we also establish pointwise bounds of the derivatives of the green functions under a regularity assumption on the l 1 mean oscillations of the coefficients

mixed boundary value problems for the stokes system we prove the well posedness of the mixed problem for the stokes system in a class of lipschitz domains in n n 3 the strategy is to reduce the original problem to a boundary integral equation and we establish certain new rellich type estimates which imply that the intervening boundary integral operator is semi fredholm we then prove that its index is zero by performing a homotopic deformation of it onto an operator related to the lame system which has recently been shown to be invertible

a finite element boundary element method for three dimensional large displacement fluid structure interaction abstract this paper presents a hybrid finite element boundary element method for fluid structure interaction simulations of inflatable structures the flow model consists of the steady stokes equation which admits a boundary integral formulation the structure is represented by a kirchhoff love shell the boundary element approximation of the stokes equation reduces the flow problem to an integral equation on the actual structure configuration thus obviating the need for volumetric meshing of the strongly deforming fluid domain the stokes model moreover exhibits a lubrication effect that acts as an intrinsic mechanism to treat the ubiquitous self contact that occurs in inflation problems the aggregated fluid structure interaction problem composed of the boundary integral equation and the kirchhoff love shell connected by dynamic and kinematic interface conditions is approximated by means of isogeometric discretizations to accommodate the smoothness requirements on the approximation spaces imposed by the flexural rigidity in the kirchhoff love shell and to provide an accurate and smooth representation of the boundary for the boundary element method auxiliary results presented in this paper are 1 a parametrization free kirchhoff love formulation 2 establishment of a cubic relationship between distance and tractions due to the lubrication effect and 3 the interpretation of the lagrange multiplier pertaining to fluid incompressibility as the total excess pressure

stability of the bakry emery theorem on rn abstract we establish quantitative stability estimates for the bakry emery bound on logarithmic sobolev and poincare constants of uniformly log concave measures more specifically we show that if a 1 uniformly log concave measure has almost the same logarithmic sobolev or poincare constant as the standard gaussian measure then it almost splits off a gaussian factor our results are dimension free leading to dimension free stability estimates for gaussian concentration of lipschitz functions the proofs are based on stein s method optimal transport and an approximate integration by parts identity relating measures and near extremals in the associated functional inequality

hardy spaces and the neumann problem in l p for laplace s equation in lipschitz domains on donne des resultats optimaux pour la resolubilite du probleme de neumann dans des domaines de lipschitz a donnees dans l p on obtient des resultats du point extreme correspondant pour des espaces de hardy

comparisons and bounds for expected lifetimes of reliability systems sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with independent and either identically or non identically distributed lifetimes are expressed in terms of expected lifetimes of components similar evaluations are concluded for the respective mean residual lifetimes in the iid case improved inequalities dependent on a concentration parameter connected to the gini dispersion index are obtained the results can be used to compare systems with component lifetimes ordered in the convex ordering in the inid case some refined bounds are derived in terms of the expected lifetimes of series systems of smaller sizes and the expected lifetime of single unit for the equivalent systems with iid components the latter can be further simplified in the case of weak schur concavity and schur convexity of the system generalized domination polynomial

a refined convergence result in homogenization of second order parabolic systems abstract we derive the sharp o e convergence rate in l 2 0 t l q 0 q 0 2 d d 1 in periodic homogenization of second order parabolic systems with bounded measurable coefficients in lipschitz cylinders this extends the corresponding result for elliptic systems established in 20 to parabolic systems and improves the corresponding result in l 2 settings derived in 7 28 for second order parabolic systems with time dependent coefficients