parabolic muckenhoupt weights in the euclidean space abstract we introduce a parabolic analogue of muckenhoupt s a p class we show that these weights satisfy a reverse holder type inequality and also prove a john nirenberg inequality for a related bmo type class both results are multidimensional generalizations of known one dimensional results as an application of our methods we extend a two dimensional weighted norm inequality of a lerner and s ombrosi to dimensions n 3

w2 p estimates for fully nonlinear elliptic equations with oblique boundary conditions abstract we study fully nonlinear elliptic equations with oblique boundary conditions we obtain a global w 2 p estimate n 0 p for viscosity solutions of such problems when the boundary of the domain is in c 2 for every 0 1

maximum principles extension problem and inversion for nonlocal one sided equations abstract we study one sided nonlocal equations of the form x 0 u x u x 0 x x 0 1 d x f x 0 on the real line notice that to compute this nonlocal operator of order 0 1 at a point x 0 we need to know the values of u x to the right of x 0 that is for x x 0 we show that the operator above corresponds to a fractional power of a one sided first order derivative maximum principles and a characterization with an extension problem in the spirit of caffarelli silvestre and stinga torrea are proved it is also shown that these fractional equations can be solved in the general setting of weighted one sided spaces in this regard we present suitable inversion results along the way we are able to unify and clarify several notions of fractional derivatives found in the literature

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

nonconforming two level discretization of stream function form of the navier stokes equations in this report we analyze a two level finite element method for the stream function formulation of the stationary navier stokes equations this report presents the two level algorithm and error analysis for the case of nonconforming elements when approximating a nonsingular solution of the stream function formulation of the navier stokes equation

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

weighted inequalities for one sided maximal functions let m be the maximal operator defined by g mb f x sup f t lg t dt f g t dt where g is a positive locally integrable function on r we characterize the pairs of nonnegative functions u v for which mb applies lp v in lp u or in weaklp u our results generalize sawyer s case g 1 but our proofs are different and we do not use hardy s inequalities which makes the proofs of the inequalities self contained

two weight weak and extra weak type inequalities for the one sided maximal operator let be the one sided maximal operator and let be a convex non decreasing function on 0 0 0 we present necessary and sufficient conditions on a couple of weight functions such that the integral inqualities of weak type and of extra weak type hold our proofs do not refer to the theory of orlicz spaces

convergence of a compact scheme for the pure streamfunction formulation of the unsteady navier stokes system this paper is devoted to the analysis of a new compact scheme for the navier stokes equations in pure streamfunction formulation numerical results using that scheme have been reported in m ben artzi e j comput phys 205 2005 pp 640 664 the scheme discussed here combines the stephenson scheme for the biharmonic operator and ideas from box scheme methodology consistency and convergence are proved for the full nonlinear system instead of customary periodic conditions the case of boundary conditions is addressed it is shown that in one dimension the truncation error for the biharmonic operator is o h 4 at interior points and o h at near boundary points in two dimensions the truncation error is o h 2 at interior points due to the cross terms and o h at near boundary points hence the scheme is globally of order four in the one dimensional periodic case and of order two in the two dimensional periodic case but of order 3 2 for one and two dimensional nonperiodic boundary conditions we emphasize in particular that there is no special treatment of the boundary thus allowing robust use of the scheme the finite element analogy of the finite difference schemes is invoked at several stages of the proofs in order to simplify their verifications

weighted variation inequalities for differential operators and singular integrals abstract we prove weighted strong q variation inequalities with 2 q for differential and singular integral operators for the first family of operators the weights used can be either sawyer s one sided a p weights or muckenhoupt s a p weights according to whether the differential operators in consideration are one sided or symmetric we use only muckenhoupt s a p weights for the second family all these inequalities hold equally in the vector valued case that is for functions with values in l for 1 as application we show variation inequalities for mean bounded positive invertible operators on l p with positive inverses

an efficient compact difference scheme for solving the streamfunction formulation of the incompressible navier stokes equations recently a new paradigm for solving the steady navier stokes equations using a streamfunction velocity formulation was proposed by gupta and kalita m m gupta j c kalita a new paradigm for solving navier stokes equations streamfunction velocity formulation j comput phys 207 2005 52 68 which avoids difficulties inherent in the conventional streamfunction vorticity and primitive variable formulations it is discovered that this formulation can reached second order accurate and obtained accuracy solutions with little additional cost for a couple of fluid flow problems in this paper an efficient compact finite difference approximation named as five point constant coefficient second order compact 5pcc soc scheme is proposed for the streamfunction formulation of the steady incompressible navier stokes equations in which the grid values of the streamfunction and the values of its first derivatives velocities are carried as the unknown variables the derivation approach is simple and can be easily used to derive compact difference schemes for other similar high order elliptic differential equations numerical examples including the lid driven cavity flow problem and a problem of flow in a rectangular cavity with the hight width ratio of 2 are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme the results obtained are compared with ones by different available numerical methods in the literature the present scheme not only shows second order accurate but also proves more effective than the existing second order compact scheme of the streamfunction formulation in the aspect of computational cost

on the coifman type inequality for the oscillation of one sided averages abstract in this paper we study the coifman type estimate for an oscillation operator related to the one sided discrete square function s we prove that for any a weight w the l p w norm of this operator and therefore the l p w norm of s is dominated by a constant times the l p w norm of the one sided hardy littlewood maximal function iterated two times for the k th commutator with a bmo function we show that k 2 iterates of the one sided hardy littlewood maximal function are sufficient

a fully locking free isogeometric approach for plane linear elasticity problems a stream function formulation in this paper we study plane incompressible elastic problems by means of a stream function formulation such that a divergence free displacement field can be computed from a scalar potential the numerical scheme is constructed within the framework of nurbs based isogeometric analysis and we take advantage of the high continuity guaranteed by nurbs basis functions in order to obtain the displacement field from the potential differentiation as a consequence the obtained numerical scheme is automatically locking free in the presence of the incompressibility constraint a discontinuous galerkin approach is proposed to deal with multiple mapped possibly multiply connected domains extensive numerical results are provided to show the method capabilities 2007 elsevier b v all rights reserved

weighted inequalities for maximal functions associated with general measures for certain positive borel measures u on r and for th any of three naturally associated maximal function operators of hardy littlewood type the weight pairs u v for which th is of weak type p p 1 p oo and of strong type p p 1 p oo are characterized only minimal assumptions are placed on u in particular u need not satisfy a doubling condition nor need it be continuous

c0 discontinuous galerkin methods for a wind driven ocean circulation model two grid algorithm abstract this paper presents a nonconforming finite element method for a streamfunction formulation of the stationary quasi geostrophic equations which describe the large scale wind driven ocean circulation the streamfunction formulation is a fourth order nonlinear pde and the nonconforming method is based on c 0 elements instead of c 1 elements existence and uniqueness of the approximation are proved and optimal error estimates in several norms of interest are demonstrated under a small data assumption two grid algorithms based on picard and newton type linearizations are then presented to efficiently resolve nonlinearities and computational results are given to demonstrate the efficiency of the algorithm the mediterranean sea example is tested with real world coastline data which illustrates the effectiveness of the two grid approach in the wind driven ocean circulation simulation

weighted inequalities for the two dimensional one sided hardy littlewood maximal function in this work we characterize the pairs of weights w v such that the one sided hardy littlewood maximal function in dimension two is of weak type p p 1 p oo with respect to the pair w v as an application of this result we obtain a generalization of the classic dunford schwartz ergodic maximal theorem for bi parameter flows of null preserving transformations

a pure compact scheme for the streamfunction formulation of navier stokes equations a pure streamfunction formulation is introduced for the numerical simulation of the two dimensional incompressible navier stokes equations the idea is to replace the vorticity in the vorticity streamfunction evolution equation by the laplacian of the streamfunction the resulting formulation includes the streamfunction only thus no inter function relations need to be invoked a compact numerical scheme which interpolates streamfunction values as well as its first order derivatives is presented and analyzed a number of numerical experiments are presented including driven and double driven cavities where the reynolds numbers are sufficiently large leading to symmetry breaking of asymptotic solutions

digital filters with implicit interpolated output the composition of filtering and interpolation operators is applied to the design of digital filters that optionally may perform real time incommensurate sampling rate conversion this problem arises in applications where the interpolation times may not be known a priori and are calculated in real time the proposed interpolating filter operators allow the designer to control the interpolation error through a trade off between computing time and accuracy the flexibility of the design is exemplified on a few digital communication applications square root raised cosine filters for controlling the intersymbol interference through pulse shaping a bandpass filter and a differentiator

extended window interpolation applied to digital filter design this paper develops a procedure for the design of frequency selective interpolation operators that can be computed and saved once and for all these operators are used to design real time digital operators interpolators fir differentiators iir filters and composed interpolation and filtering operators each real time operator is a matrix relating sets of data points to sets of interpolated values since these matrices are characterized by low norms they permit reduced word implementations and are suitable for real time processing with array processors and massively parallel machines the design of the interpolation operators uses windows that unlike traditional approaches extend beyond the data interval up to the length permitted by the dimensionality theorem a new form of the dimensionality theorem is used to minimize the minimax interpolation error within a predetermined frequency range which may be either the passband of the antialiasing filter or the passband of an analog prototype filter the main application presented in the paper is the design of combined digital filters and interpolators which will be referred to as interpolating filters the frequency responses of such filters as well as the interpolated time responses almost coincide with those of the corresponding analog prototypes

stability and convergence of efficient navier stokes solvers via a commutator estimate for strong solutions of the incompressible navier stokes equations in bounded domains with velocity specified at the boundary we establish the unconditional stability and convergence of discretization schemes that decouple the updates of pressure and velocity through explicit time stepping for pressure these schemes require no solution of stationary stokes systems nor any compatibility between velocity and pressure spaces to ensure an inf sup condition and are representative of a class of highly efficient computational methods that have recently emerged the proofs are simple based upon a new sharp estimate for the commutator of the laplacian and helmholtz projection operators this allows us to treat an unconstrained formulation of the navier stokes equations as a perturbed diffusion equation c 2006 wiley periodicals inc

convergence of the lacunary ergodic cesaro averages abstract let t be a positive linear operator with positive inverse we consider in this paper the ergodic cesaro averages a n f 0 1 and the ergodic cesaro maximal operator associated to t for lebesgue spaces l p it is known that the good range for the convergence of the cesaro averages and the boundedness of the maximal operator is 1 p in this paper we study the convergence of a n k f where n k is a lacunary sequence and the boundedness of its associated ergodic maximal operator we get positive results in the range 1 p 1 1 we use transference arguments which leads to us to study in depth weighted inequalities of the lacunary cesaro maximal operator in the setting of the integers and in the setting of the real line

matrix operators for numerically stable representation of stiff linear dynamic systems a new transformation having features similar to the laplace transform but numerically oriented is developed from the chebyshev polynomials theory signals are represented as vectors of chebyshev coefficients and linear subsystems as precomputed matrices the original problem is preprocessed only once to yield matrix invariants for fast recurrent computations theoretical implications of the exact digitizing of a tenth order transfer function and the reduced order modeling of a stiff system are discussed

one sided extrapolation at infinity and singular integrals in this paper we prove on one hand extrapolation from infinity for the one sided classes ap a p q a p q and on the other hand the bmo boundedness for one sided singular integrals we also provide several applications of our results

one sided fractional derivatives fractional laplacians and weighted sobolev spaces abstract we characterize one sided weighted sobolev spaces w 1 p r where is a one sided sawyer weight in terms of a e and weighted l p limits as 1 of marchaud fractional derivatives of order similar results for weighted sobolev spaces w 2 p r n where is an a p muckenhoupt weight are proved in terms of limits as s 1 of fractional laplacians s these are bourgain brezis mironescu type characterizations for weighted sobolev spaces we also complement their work by studying a e and weighted l p limits as s 0

a unified approach to energy conservation and potential vorticity dynamics for arbitrarily structured c grids a numerical scheme applicable to arbitrarily structured c grids is presented for the nonlinear shallow water equations by discretizing the vector invariant form of the momentum equation the relationship between the nonlinear coriolis force and the potential vorticity flux can be used to guarantee that mass velocity and potential vorticity evolve in a consistent and compatible manner underpinning the consistency and compatibility of the discrete system is the construction of an auxiliary thickness equation that is staggered from the primary thickness equation and collocated with the vorticity field the numerical scheme also exhibits conservation of total energy to within time truncation error simulations of the standard shallow water test cases confirm the analysis and show convergence rates between 1st and 2nd order accuracy when discretizing the system with quasi uniform spherical voronoi diagrams the numerical method is applicable to a wide class of meshes including latitude longitude grids voronoi diagrams delaunay triangulations and conformally mapped cubed sphere meshes

a two level finite element discretization of the stream function form of the navier stokes equations abstract we analyze a two level method of discretizing the stream function form of the navier stokes equations this report presents the two level algorithm and error analysis for the case of conforming elements the two level algorithm consists of solving a small nonlinear system on the coarse mesh then solving a linear system on the fine mesh the basic result states that the error between the coarse and fine meshes are related superlinearly via as an example if the clough tocher triangles or the bogner fox schmit rectangles are used then the coarse and fine meshes are related by h o h 3 2 ln h 1 4

a priori and a posteriori error analysis for a large scale ocean circulation finite element model we consider the finite element solution of the stream function vorticity formulation for a large scale ocean circulation model first we study existence and uniqueness of solution for the continuous and discrete problems under appropriate regularity assumptions we prove that the stream function can be computed with an error of order h in h1 seminorm second we introduce and analyze an h adaptive mesh refinement strategy to reduce the spurious oscillations and poor resolution which arise when convective terms are dominant we propose an a posteriori anisotropic error indicator based on the recovery of the hessian from the finite element solution which allows us to obtain well adapted meshes the numerical experiments show an optimal order of convergence of the adaptive scheme furthermore this strategy is efficient to eliminate the oscillations around the boundary layer

an lq approach with generalized anisotropic weights of the weak solution of the oseen flow around a rotating body in the whole space abstract in the present paper we study the stationary oseen type system for flow around a rotating body we study the system in the whole three dimensional space we establish the existence and uniqueness of a weak solution in weighted l q spaces we also investigate the regularity of the solutions

extrapolation of weights revisited new proofs and sharp bounds abstract we use an appropriate factorization of the a p weights to give another proof of the extrapolation theorem of rubio de francia it provides sharp bounds in terms of the a p constant of the weights then we extend the result to more general settings including off diagonal and partial range extrapolation among the applications we prove by iteration a multivariable extrapolation theorem and give a sharp bound for calderon zygmund operators on l p w for weights in a q q p

numerical computations of viscous incompressible flow problems using a two level finite element method we consider two level finite element discretization methods for the stream function formulation of the navier stokes equations the two level method consists of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh the basic result states that the errors between the coarse and fine meshes are related superlinearly this paper demonstrates that the two level method can be implemented to approximate efficiently solutions to the navier stokes equations two fluid flow calculations are considered to test problems which have a known solution and the driven cavity problem stream function contours are displayed showing the main features of the flow

on weights satisfying parabolic muckenhoupt conditions abstract this note collects results related to parabolic muckenhoupt a p weights for a doubly nonlinear parabolic partial differential equation a general approach is proposed which extends the theory beyond the quadratic growth case in particular the natural parabolic geometry for the equation and the unavoidable time lag are incorporated in the definitions and results the limiting muckenhoupt conditions of a type are also discussed and several open questions are posed

weighted norm inequalities for the riemann liouville and weyl fractional integral operators caracterisation des fonctions poids pour lesquelles l operateur integral fractionnaire de riemann liouville d ordre 0 est borne

error estimates of proper orthogonal decomposition eigenvectors and galerkin projection for a general dynamical system arising in fluid models we study estimates for proper orthogonal decomposition eigenvectors and eigenvalues as well as error estimates between the exact solution of a 2d navier stokes model and the numerical approach when the proper orthogonal decomposition method is considered these estimates are also extended when bifurcation diagram are calculated using the so called p pod or spod methods with a new cut off criterion to minimize noisy modes produced by the p pod method

finite element technique for optimal pressure recovery from stream function formulation of viscous flows presentation d un algorithme de recouvrement de la pression base sur une analyse generale de la converge de la solution en elements finis de l equation de navier stokes

a c0 discontinuous galerkin method for the stationary quasi geostrophic equations of the ocean abstract this work concerns the development of a finite element algorithm for the stationary quasi geostrophic equations to treat the large scale wind driven ocean circulation the algorithm is developed based on the streamfunction formulation involving fourth order gradients of the streamfunction here we examine the adaptation of a relatively inexpensive nonconforming method based on c 0 basis functions we develop the variational form of the method and establish consistency the method weakly enforces continuity of the normal flux across interelement boundaries and stabilization is achieved via nitsche s method explicit expression for the choice of the stabilization parameter is derived moreover the theoretical error estimate for the linear stommel munk model is performed numerical results from several benchmark problems on rectangular and curved domains are provided to demonstrate the accuracy and robustness of the method we also provide the mediterranean sea example to demonstrate the capability of the approach to the wind driven ocean circulation simulation

mean boundedness and littlewood paley for separation preserving operators suppose that q m u is a o finite measure space 1 p oo and t lp lp is a bounded invertible separation preserving linear operator such that the linear modulus of t is mean bounded we show that t has a spectral representation formally resembling that for a unitary operator but involving a family of projections in lp which has weaker properties than those associated with a countably additive borel spectral measure this spectral decomposition for t is shown to produce a strongly countably spectral measure on the dyadic sigma algebra of t7 and to furnish lp with abstract analogues of the classical littlewood paley and vector valued m riesz theorems for p z

comments on further improvements in digitizing continuous time filters this correspondence points out that an algorithm proposed by c wan and a m schneider see ibid vol 45 no 3 p 533 42 march 1997 as a new digitizing method is in fact an extension of the linear interpolation design unlike previously published extensions which incorporate the interpolation step into the s to z domain mapping step this algorithm cascades the interpolator and the analog filter original design formulas derived for a rigorous comparison support the assertion that the above algorithm yields less accurate results than the other interpolation designs

weighted inequalities for the one sided hardy littlewood maximal functions let m f x suph 0 l h jx h t 1 idt denote the one sided maximal function of hardy and littlewood for w x 0 on r and 1 0 and a v ll p then m is bounded from lp v to lp w if and only if m x a w 0 the corresponding weak type inequality is also characterized further properties of a weights such as a a e and a p a a1 p are established

a two level finite element discretization of the streamfunction formulation of the stationary quasi geostrophic equations of the ocean in this paper we proposed a two level finite element discretization of the nonlinear stationary quasi geostrophic equations which model the wind driven large scale ocean circulation optimal error estimates for the two level finite element discretization were derived numerical experiments for the two level algorithm with the argyris finite element were also carried out the numerical results verified the theoretical error estimates and showed that for the appropriate scaling between the coarse and fine mesh sizes the two level algorithm significantly decreases the computational time of the standard one level algorithm

a co volume scheme for the rotating shallow water equations on conforming non orthogonal grids a co volume scheme is introduced for the rotating shallow water equations in which both velocity components are specified on cell edges and the thickness variables evolve on both the primary and the dual cell centers the scheme applies to generic conforming and non orthogonal staggered grids including the widely used lat lon quadrilateral grids and the delaunay voronoi tessellations it can be viewed either as coupled c grid schemes on the primary and dual meshes or as an generalization of the traditional e grid scheme on a new non overlapping grid linear dispersive wave analysis shows that the dispersive relations resolved by either the primary or the dual mesh of a uniform quadrilateral staggered grid is the same as those of the z grid scheme the total wavenumber space resolved by the staggered grid is twice as large on which the co volume behaves exactly like the e grid scheme on a uniform hexagon triangular staggered grid the co volume has two steady modes and two inertial gravity modes on the hexagonal mesh and one steady mode two inertial gravity modes and two spurious modes on the triangular mesh on the wavenumber space resolved by either the hexagonal or the triangular mesh the inertial gravity wave modes remain positive and largely monotone for the nonlinear shallow water equations the co volume scheme is shown to preserve the potential vorticity dynamics and the total energy exactly numerical results are presented to corroborate and supplement the analyses

the optimal convergence rate of a c1 finite element method for non smooth domains we establish optimal up to arbitrary e 0 convergence rates for a finite element formulation of a model second order elliptic boundary value problem in a weightedh 2 sobolev space with 5th degree argyris elements this formulation arises while generalizing to the case of non smooth domains an unconditionally stable scheme developed by liu et al j g liu j liu r l pego stability and convergence of efficient navier stokes solvers via a commutator estimate comm pure appl math 60 2007 pp 1443 1487 for the navier stokes equations we prove the optimality for both quasiuniform and graded mesh refinements and provide numerical results that agree with our theoretical predictions

numerical simulations of a two layer quasi geostrophic equation of the ocean our object in this article is to present some numerical schemes for a two layer quasi geostrophic model of the ocean and to study the stability of these schemes we prove the unconditional stability of our numerical schemes numerical results from a wind driven two layer quasi geostrophic model of the ocean using these schemes are also presented

weighted norm inequalities involving gradients let then for certain weight functions u and v and indices p q it is shown that t f q u c grad f p v q n holds for l p q and u v l this reduces to a result of m weiss in addition we establish n dimensional weighted hardy littlewood type inequalities ofthe form for large classes of weights

maximal averages over surfaces letmf x supt 0 f t d x denote the maximal operator associated with surface measured on a smooth surfaces we prove that ifsis convex and has finite order contact with its tangent lines then m is bounded onlp rn p 2 if and only ifd x h 1 l1 loc s for all tangent planeshnot passing through the origin letm f x supt 0 f t d x be the maximal operator associated with a nonisotropic dilation tof surface measured we prove that m often behaves far better than m due to a rotational curvature in the time parametert

a comparison of two numerical methods for integrating a quasi geostrophic multilayer model of ocean circulations to study the feasibility of using the finite elements method for ocean modelling a quasi geostrophic eddy resolving general circulation model has been driven using either a classical finite differences technique or a finite elements technique this feasibility has been clearly demonstrated and a comparison of the models performances shows that for simulations of realistic basins the finite elements model cpu cost is only four times the finite difference model cost

a central difference scheme for a pure stream function formulation of incompressible viscous flow we present a numerical scheme for incompressible viscous flow formulated as an equation for the stream function the pure stream function formulation obviates the difficulty associated with vorticity boundary conditions the resulting biharmonic equation is discretized with a compact scheme and solved with an algebraic multigrid solver the advection of vorticity is implemented with a high resolution central scheme that remains stable and accurate in the presence of large gradients the accuracy and robustness of the method are demonstrated for high reynolds number flows in a lid driven cavity

weighted lebesgue and lorentz norm inequalities for the hardy operator characterizations are obtained for those pairs of weight functions w v for which the hardy operator tf x j fo f s ds is bounded from the lorentz space l s 0 oo v dx to lp o oo w dx 0 p q r s oo the modified hardy operators t f x x 17tf x for q real are also treated 1 introduction we characterize weighted lebesgue and lorentz norm inequalities for the hardy operator tf x fox f t dt and the modified hardy operators t1 f x

spline based finite element method for the stationary quasi geostrophic equations on arbitrary shaped coastal boundaries abstract this work concerns a b spline based finite element algorithm for the stationary quasi geostrophic equations to treat the large scale wind driven ocean circulation on arbitrary shaped domains the algorithm models arbitrary shaped coastal boundaries on intra element or embedded boundaries dirichlet boundary conditions on the embedded boundaries are weakly imposed and stabilization is achieved via nitsche s method we employ a hierarchical local refinement approach to improve the geometrical representation of curved boundaries results from several benchmark problems on rectangular and curved domains are provided to demonstrate the accuracy and robustness of the method we also provide the mediterranean sea example that illustrates the effectiveness of the approach in the wind driven ocean circulation simulation

weights for commutators of the one sided discrete square function the weyl fractional integral and other one sided operators the purpose of this paper is to prove strong type inequalities with one sided weights for commutators with symbol b bmo of several one sided operators such as the one sided discrete square function the one sided fractional operators or one sided maximal operators given by the convolution with a smooth function we also prove that b bmo is a necessary condition for the boundedness of commutators of these one sided operators

a posteriori analysis of a b spline based finite element method for the stationary quasi geostrophic equations of the ocean abstract we provide a posteriori error analysis of a b spline based finite element method for the streamfunction formulation of the stationary quasi geostrophic equations to model the large scale wind driven ocean circulation the analysis gives rise to a posteriori error estimator for more efficient and accurate modeling of a strong western boundary layer via adaptive local refinement of the computational geometries to verify the capability of the error estimator we use hierarchical b splines in conjunction with dorfler marking strategy numerical studies are performed for several benchmark examples on rectangular and l shape ocean geometries

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

a singular boundary value problem for uniformly elliptic operators abstract strong solvability in the sobolev space w 2 p is proved for the oblique derivative problem j i 1 n a ij x d ij u f x almost every where in u l x u x in the trace sense on in the case when the vector field l x has a contact of infinite order with at the points of some non empty subset e

stable partial pade approximations for reduced order trnsfer functions while the pade approximation can often be used to produce good reduced order transfer functions the method suffers from the disadvantage that a stable reduced order model is not always obtained for an original model that is stable a method is described for obtaining stable partial pade approximation reduced order models the method permits the determination of the effect of changes in the coefficients in the partial pade approximation on the poles of the reduced order transfer function by means of standard root locus plots

generalized hormander s conditions commutators and weights we present a general framework to deal with commutators of singular integral operators with bmo functions hormander type conditions associated with young functions are assumed on the kernels coifman type estimates weighted norm inequalities and two weight estimates are considered we give applications to homogeneous singular integrals fourier multipliers and one sided operators

error estimates of b spline based finite element methods for the stationary quasi geostrophic equations of the ocean abstract this paper presents theoretical error estimates of b spline based finite element methods for the streamfunction formulation of the stationary quasi geostrophic equations which describe the large scale wind driven ocean circulation we introduce variational formulations of the streamfunction formulation inspired by the interior penalty discontinuous galerkin method dirichlet boundary conditions are weakly enforced in the formulations and stabilizations are achieved via nitsche s method existence and uniqueness of the approximation are proved and optimal error estimates in the energy norm are demonstrated under a small data assumption numerical experiments are performed to verify the theoretical error estimates on rectangular and l shape geometries

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

two grid discretizations with backtracking of the stream function form of the navier stokes equations we analyze a two grid finite element method with backtracking for the stream function formulation of the stationary navier stokes equations this two grid method involves solving one small nonlinear coarse mesh system one linearized system on the fine mesh and one linear correction problem on the coarse mesh the algorithm and error analysis are presented

b spline based finite element method for the stationary quasi geostrophic equations of the ocean abstract we present a b spline based conforming finite element method of the streamfunction formulation of the stationary one layer quasi geostrophic equations for the study of the large scale wind driven ocean circulation the method encompasses standard simplifications of these equations in particular the linear stommel and stommel munk models a variational form of the method is developed and its consistency is established in this formulation dirichlet boundary conditions are enforced only weakly and stabilization is achieved via nitsche s method stability parameters are evaluated by solving a local generalized eigenvalue problem on the dirichlet boundary and by monitoring the condition number of the resulting linear systems comparisons of the results from our simulations with previously published results and convergence studies lead us to conclude that our finite element discretization is accurate

weak and strong type estimates for the multilinear pseudo differential operators abstract in this paper we investigate the boundedness of the multilinear pseudo differential operator t first we establish the local exponential decay estimates for t in terms of the corresponding commutators t b we obtain the local subexponential decay estimates secondly we derive the weighted mixed weak type inequality for t which parallels sawyer s conjecture for calderon zygmund operators and covers the endpoint weighted inequalities last but not least we present the sharp weighted estimates for t and t b it is worth mentioning that our results are totally new even in the linear case

the poincare problem in l p sobolev spaces i codimension one degeneracy we study a degenerate oblique derivative problem in sobolev spaces w2 p p 1 for uniformly elliptic operators with lipschitz continuous coefficients the vector field prescribing the boundary condition becomes tangential to at the points of a non empty set and is of emergent type

some one sided estimates for oscillatory singular integrals abstract the purpose of this paper is to establish some one sided estimates for oscillatory singular integrals the boundedness of certain oscillatory singular integrals on weighted hardy spaces h 1 w is proved it is here also shown that the h 1 w theory of oscillatory singular integrals above cannot be extended to the case of h q w when 0 q 1 and w a p a wider weight class than the classical muckenhoupt class furthermore a criterion on the weighted l p boundedness of the oscillatory singular integral is given

on the sharpness of certain local estimates for projections into finite element spaces influence of a re entrant corner in a plane polygonal domain with a reentrant corner consider a homogeneous dirichlet problem for poisson s equation au f with f smooth and the corresponding galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi uniform uniformly regular triangulations with the diameter of each element compara