existence uniqueness and l q estimates for the stokes problem in an exterior domain as is well known the study of the properties of solutions to the stokes system plays an essential role in the mathematical theory of viscous fluid flows governed by the navier stokes equations it is not art overstatement to say that existence uniqueness and a priori estimates in sobolev spaces for the stokes system are fundamental in every basic question related to the navier stokes equations such as existence regularity asymptotic behavior in time etc see e g ladyzhenskaya 1969 solonni ov 1977 and te am 1977 so far however the stokes system has been fully analyzed only for bounded domains see sobolevskn 1960 ladvznenskaya 1959 solonnu ov 1960 vorovlch yot oowcr 1961 cattabrma 1961 in particular in the paper of cattabriga a complete treatment is given in the sobotev spaces w l 1 1 q c for space dimension n 3 cattabriga s results essentially state that if 2 is a bounded domain in r a of class c m m max l 2 2 l 1 then given f e wt q y2 3 gc wt l q o q e wl 2 1 q q 8o a 1 q there exists one and only one distributional solution v c w1 z q q 3 p e wt l q o to the stokes system

ordered sets with the standardizing property and straightening laws for algebras of invariants abstract in math z 176 1981 359 374 i explicitly determined the invariants of a certain class of unipotent group actions and obtained a positive partial answer to hilbert s 14th problem for nonreductive groups the class of groups for which the method worked remained quite obscure theorem 4 2 of the present paper gives a precise description of the cases where the algebras of invariants are spanned by standard bitableaux hence have a straightening law the unipotent groups in question radizielle untergruppen of gln correspond up to conjugation to finite partially ordered sets the promised description is done by properties of the ordered sets that are easy to test this is another example where combinatorial methods are important for the theory of invariants

factor analysis for non normal variables factor analysis for nonnormally distributed variables is discussed in this paper the main difference between our approach and more traditional approaches is that not only second order cross products like covariances are utilized but also higher order cross products it turns out that under some conditions the parameters factor loadings can be uniquely determined two estimation procedures will be discussed one method gives best generalized least squares bgls estimates but is computationally very heavy in particular for large data sets the other method is a least squares method which is computationally less heavy in one example the two methods will be compared by using the bootstrap method in another example real life data are analyzed

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

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

quadratic prediction of factor scores factor scores are naturally predicted by means of their conditional expectation given the indicators y under normality this expectation is linear in y but in general it is an unknown function of y ii is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function of y

for the vorticity velocity pressure form of the navier stokes equations on a bounded plane domain with corners abstract we show existence and regularity for the boundary value problems of the navier stokes equations with non standard bcs on a bounded plane domain with non convex corners we assign the vorticity value 0 and the velocity normal component u n u 0 n over the non convex corner the dynamic pressure value p u 2 2 p 0 over inflow and outflow boundaries and so on we construct the corner singularity functions for the stokes operator with zero vorticity and velocity normal component bcs subtract its leading singularity from the solution by defining the coefficient of the singularity and show increased regularity for the remainder the solution is determined by the smoother part and the coefficients of the singularities it is seen from the singularity that the dynamic pressure has a transition layer that changes the sign at 2 in the domain the obtained results can be applied to general polygonal domains and the cavity flows

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

boundary value problems for the laplacian in convex and semiconvex domains abstract we study the fully inhomogeneous dirichlet problem for the laplacian in bounded convex domains in r n when the size smoothness of both the data and the solution are measured on scales of besov and triebel lizorkin spaces as a preamble we deal with the dirichlet and regularity problems for harmonic functions in convex domains with optimal nontangential maximal function estimates as a corollary sharp estimates for the green potential are obtained in a variety of contexts including local hardy spaces a substantial part of this analysis applies to bounded semiconvex domains i e lipschitz domains satisfying a uniform exterior ball condition

spectral analysis of the fourth moment matrix the fourth moment of a random vector is a matrix whose elements are all moments of order four which can be obtained from the random vector itself in this paper we give a lower bound for its dominant eigenvalue and show that its eigenvectors corresponding to positive eigenvalues are vectorized symmetric matrices fourth moments of standardized and exchangeable random vectors are examined in more detail

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

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

consistent estimation of linear panel data models with measurement error abstract measurement error causes a bias towards zero when estimating a panel data linear regression model the panel data context offers various opportunities to derive instrumental variables allowing for consistent estimation we consider three sources of moment conditions i restrictions on the covariance matrix of the errors in the equations ii nonzero third moments of the regressors and iii heteroskedasticity and nonlinearity in the relation between the error ridden regressor and another error free regressor in simulations these approaches appear to work well

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

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

asymptotic chi square tests for a large class of factor analysis models asymptotic behavior of the test statistics for three types of 2 goodness of fit tests is investigated for the factor analysis model with linearly or nonlinearly restricted factor loadings under weak assumptions on the factor vector and the error vector in particular the limiting 2 result for the three tests is shown to hold for the factor vector and for the error vector with any distribution having finite second order moments provided that the components of the error vector are independent as special cases the result holds for exploratory and confirmatory factor analysis models and for certain non normal structural equation models

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

matrix algebra for higher order moments abstract a large part of statistics is devoted to the estimation of models from the sample covariance matrix the development of the statistical theory and estimators has been greatly facilitated by the introduction of special matrices such as the commutation matrix and the duplication matrix and the corresponding matrix algebra some more extensive models require however estimation based on higher order moments typically third and fourth order moments an example is the popular kenny judd model that includes interactions between latent variables this paper introduces some special matrices that can be used to simplify the model expressions for third fourth and higher order moments gives some relationships between these matrices and related matrices and gives some formulas for kronecker products of three and four matrices the theory is applied to derive convenient expressions for third and fourth order moments of some structural equation models

concise formulae for the cumulant matrices of a random vector concise formulae are given for the cumulant matrices of a real valued zero mean random vector up to order 6 in addition to usual matrix operations they involve only the kronecker product the vec operator and the commutation matrix orders 5 and 6 are provided here for the first time the same method as provided in the paper can be applied to compute higher orders an immediate consequence of these formulae is to return 1 upper bounds on the rank of the cumulant matrices and 2 the expression of the sixth order moment matrix of a gaussian vector due to their conciseness the proposed formulae also have a computational advantage as compared to the repeated use of leonov and shiryaev formula

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

vorticity velocity pressure formulation for stokes problem we propose a three field formulation for efficiently solving a twodimensional stokes problem in the case of nonstandard boundary conditions more specifically we consider the case where the pressure and either normal or tangential components of the velocity are prescribed at some given parts of the boundary the proposed computational methodology consists in reformulating the considered boundary value problem via a mixed type formulation where the pressure and the vorticity are the principal unknowns while the velocity is the lagrange multiplier the obtained formulation is then discretized and a convergence analysis is performed a priori error estimates are established and some numerical results are presented to highlight the perfomance of the proposed computational methodology

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

one problem of the navier type for the stokes system in planar domains we study the problem u f u f u g u g in u gu g h h on for a bounded simply connected lipschitz domain in the plane for f 0f 0 g 0g 0 g lp g lp h lq h lq we study a solution in the sense of a nontangential limit for f ws 1 q r2 f ws 1 q r2 g ws q g ws q g wt 1 p p g wt 1 p p h ws 1 q q h ws 1 q q with t s 1t s 1 we prove the existence of a unique solution u wt p r2 ws q u wt p r2 ws q for f bs 1q r r2 g bsq r g bt 1 pp h bs 1 qq r with t s 1t s 1 we prove the existence of a unique solution u btp r2 bsq r for f ck 1 r2 g ck h ck h ck g ck 1 g ck 1 we prove the existence of a unique solution u ck 1 r2 ck

higher moment estimators for linear regression models with errors in the variables abstract this paper proposes consistent instrumental variable estimators for linear regression models with errors in the variables that require no extraneous information these estimators are based on sample moments of order higher than two while similar estimators proposed previously in the literature seem to be quite erratic our experimental f findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type i errors of standard tests in many typical situations of economic analyses tests for the presence of errors in the variables are also described

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

weighted estimates in l 2 for laplace s equation on lipschitz domains let c r d d 3 be a bounded lipschitz domain for laplace s equation au 0 in q we study the dirichlet and neumann problems with boundary data in the weighted space l 2 leader where q q q 0 q 0 is a fixed point on and da denotes the surface measure on we prove that there exists e e 0 2 such that the dirichlet problem is uniquely solvable if 1 d d 3 e and the neumann problem is uniquely solvable if 3 d e a d 1 if q is a c 1 domain one may take e 2 the regularity for the dirichlet problem with data in the weighted sobolev space l 2 1 d is also considered finally we establish the weighted l 2 estimates with general ap weights for the dirichlet and regularity problems

the neumann problem and helmholtz decomposition in convex domains we show that the neumann problem for laplace s equation in a convex domain with boundary data in lp is uniquely solvable for 1 p as a consequence we obtain the helmholtz decomposition of vector fields in lp rd

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

lp theory for stokes and navier stokes equations with navier boundary condition abstract this work was intended as an attempt at studying stationary stokes and navier stokes problem with navier boundary conditions 1 3 we wish to investigate some results of existence uniqueness and regularity of solutions in hilbert case and in l p theory

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

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

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

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

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

moment testing for interaction terms in structural equation modeling starting with kenny and judd psychol bull 96 201 210 1984 several methods have been introduced for analyzing models with interaction terms in all these methods more information from the data than just means and covariances is required in this paper we also use more than just first and second order moments however we are aiming to adding just a selection of the third order moments the key issue in this paper is to develop theoretical results that will allow practitioners to evaluate the strength of different third order moments in assessing interaction terms of the model to select the third order moments we propose to be guided by the power of the goodness of fit test of a model with no interactions which varies with each selection of third order moments a theorem is presented that relates the power of the usual goodness of fit test of the model with the power of a moment test for the significance of third order moments the latter has the advantage that it can be computed without fitting a model the main conclusion is that the selection of third order moments can be based on the power of a moment test thus assessing the relevance in the analysis of different sets of third order moments can be computationally simple the paper gives an illustration of the method and argues for the need of refraining from adding into the analysis an excess of higher order moments

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

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

the neumann problem in lp on lipschitz and convex domains abstract given p 2 and a bounded lipschitz domain we obtain a necessary and sufficient condition for the solvability of the neumann problem for laplace s equation u 0 in with boundary data in l p as a result we show that the l p neumann problem on convex domains in r d is solvable for 1 p if d 2 for 1 p 4 if d 3 and for 1 p 3 e if d 4

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

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

potential theory on lipschitz domains in riemannian manifolds the case of dini metric tensors we study the applicability of the method of layer potentials in the treatment of boundary value problems for the laplace beltrami operator on lipschitz sub domains of riemannian manifolds in the case when the metric tensor g jk dx j desk has low regularity under the assumption that g jk x g jk y c x y where the modulus of continuity satisfies a dini type condition we prove the well posedness of the classical dirichlet and neumann problems with l p boundary data for sharp ranges of p s and with optimal nontangential maximal function estimates

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

identification and estimation of polynomial errors in variables models abstract methods of estimation of regression coefficients are proposed when the regression function includes a polynomial in a true regressor which is measured with error two sources of additional information concerning the unobservable regressor are considered either an additional indicator of the regressor itself measured with error or instrumental variables which characterize the systematic variation in the true regressor in both cases estimators are constructed by relating moments involving the unobserved variables to moments of observables these relations lead to recursion formulae for computation of the regression coefficients and nuisance parameters e g moments of the measurement error consistency and asymptotic normality of the estimated coefficients is demonstrated and consistent estimators of the asymptotic covariant matrices are provided

boundary layer methods for lipschitz domains in riemannian manifolds abstract we extend to the variable coefficient case boundary layer techniques that have been successful in the treatment of the laplace equation and certain other constant coefficient elliptic partial differential equations on lipschitz domains in euclidean space we treat the laplace operator on lipschitz domains in a manifold with c 1 metric tensor and study the dirichlet neumann and oblique derivative boundary problems

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

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