the capelli identity tube domains and the generalized laplace transform the key result in this paper is a proof of a large class of identities generalizing the capelli identity cl the capelli identity is a centerpiece of 19th century invariant theory it asserts the equality of two differential operators on the n2 dimensional space m n r of n x n real matrices let e denote the ijth elementary matrix let xii denote the linear functions on m n r dual to e and write 3 for the partial differential operator a ax then this identity says

the primal dual active set strategy as a semismooth newton method this paper addresses complementarity problems motivated by constrained optimal control problems it is shown that the primal dual active set strategy which is known to be extremely efficient for this class of problems and a specific semismooth newton method lead to identical algorithms the notion of slant differentiability is recalled and it is argued that the max function is slantly differentiable in lp spaces when appropriately combined with a two norm concept this leads to new local convergence results of the primal dual active set strategy global unconditional convergence results are obtained by means of appropriate merit functions

on the quadratic finite element approximation to the obstacle problem in this paper we obtain the error bound o left h frac 32 epsilon right for any epsilon 0 for the piecewise quadratic finite element approximation to the obstacle problem without the hypothesis that the free boundary has finite length see 3

convergence of nonconforming multigrid methods without full elliptic regularity we consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity we prove that there is a bound 1 for the contraction number of the w cycle algorithm which is independent of mesh level provided that the number of smoothing steps is sufficiently large we also show that the symmetric variable v cycle algorithm is an optimal preconditioner

solitary waves and n coupled nonlinear equations we present analytic sets of n solitary waves as solutions of n coupled nonlinear schrodinger and of n coupled quadratic equations for which the nonlinear coupling parameters of the coupled equations can take up wide ranges of values the coupled equations may not be integrable in the usual sense but have analytic solitary waves and are solvable for the given initial conditions prescribed by the analytic solutions potential applications of these solitary waves are discussed

boundary orbit strata and faces of invariant cones and complex ol shanskiĭ semigroups let d g k be an irreducible hermitian symmetric domain then g is contained in a complexification gc and there exists a closed complex subsemigroup g gc characterised by fact that all holomorphic discrete series representations of g extend holomorphically to the socalled minimal ol shanskiuo semigroup parallel to the classical theory of boundary strata for the symmetric

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

inhomogeneous dirichlet boundary condition in the a posteriori error control of the obstacle problem abstract we study a posteriori error control of finite element approximation of the elliptic obstacle problem with nonhomogeneous dirichlet boundary condition the results in the article are two fold firstly we address the influence of the inhomogeneous dirichlet boundary condition in residual based a posteriori error control of the elliptic obstacle problem secondly by rewriting the obstacle problem in an equivalent form we derive a posteriori error bounds which are in simpler form and efficient to accomplish this we construct and use a post processed solution u h of the discrete solution u h which satisfies the exact boundary conditions sharply although the discrete solution u h may not satisfy we propose two post processing methods and analyze them namely the harmonic extension and a linear extension the theoretical results are illustrated by the numerical results

generalized lorentz invariance and solitary waves for coupled nonlinear klein gordon equations a generalized lorentz transformation that preserves the invariance of a nonlinear klein gordon equation is presented and is used to extend the set of solitary wave solutions for a special set of n coupled nonlinear schrodinger equations to become solutions of the corresponding set of coupled nonlinear klein gordon equations

a minimal energy tracking method for non radially symmetric solutions of coupled nonlinear schrodinger equations we aim at developing methods to track minimal energy solutions of time independent m component coupled discrete nonlinear schrodinger dnls equations we first propose a method to find energy minimizers of the 1 component dnls equation and use it as the initial point of the m component dnls equations in a continuation scheme we then show that the change of local optimality occurs only at the bifurcation points the fact leads to a minimal energy tracking method that guides the choice of bifurcation branch corresponding to the minimal energy solution curve by combining all these techniques with a parameter switching scheme we successfully compute a non radially symmetric energy minimizer that can not be computed by existing numerical schemes straightforwardly

homogeneous tuples of multiplication operators on twisted bergman spaces letbthe bergman kernel on the domain n mofn mcontractive complex matrices m n 1 let w wn mbe the associated wallach set consisting of the 0 for whichb m n is non negative definite and hence the reproducing kernel of a functional hilbert space h for w we examine themn tuplem of operators on h whose components are multiplications by themnco ordinate functions this tuple is homogeneous with respect to the group action ofpsu n m on the matrix ball utilising this group action we are able to determine the set of all w for which i m is bounded and for which ii m is bounded and jointly subnormal further the joint taylor spectrum ofm is determined for all as in i the subnormality ofm turns out to be closely tied with the representation theory ofpsu n m namely m is subnormal precisely when the natural projective representation ofpsu n m on the twisted bergman space h is a subrepresentation of an induced representation of multiplicity 1 finally we examine the values of for whichm admits its taylor spectrum as ak spectral set and obtain incomplete results on this question this question remains open and interesting onn 1 gaps that is for belonging to the union ofn 1 pairwise disjoint open intervals most of the techniques developed in this paper are applicable to all bounded cartan domains though we stick to the matrix domains n mfor concreteness

jordan triples and riemannian symmetric spaces we introduce a class of real jordan triple systems called jh triples and show via the tits kantor koecher construction of lie algebras that they correspond to a class of riemannian symmetric spaces including the hermitian symmetric spaces and the symmetric r spaces

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

averaging techniques yield reliable a posteriori finite element error control for obstacle problems the reliability of frequently applied averaging techniques for a posteriori error control has recently been established for a series of finite element methods in the context of second order partial differential equations this paper establishes related reliable and efficient a posteriori error estimates for the energy norm error of an obstacle problem on unstructured grids as a model example for variational inequalities the surprising main result asserts that the distance of the piecewise constant discrete gradient to any continuous piecewise affine approximation is a reliable upper error bound up to known higher order terms consistency terms and a multiplicative constant

explicit solutions with non trivial phase of the inhomogeneous coupled two component nls system in this article we construct novel explicit solutions for nonlinear schrodinger systems with spatially inhomogeneous nonlinearity by means of the lie symmetry method we focus the attention to solutions with non trivial phase which have been scarcely considered in the related literature to get started the theoretical method based on lie symmetries is exposed thus reducing the problem to the integrability of an ode the non trivial phase introduces a singular term into the ode then the method is used to construct new families of analytical solutions some illustrative examples are provided

superconvergence analysis of low order nonconforming finite element methods for variational inequality problem with displacement obstacle abstract superconvergence analysis of nonconforming finite element methods fems are discussed for solving the second order variational inequality problem with displacement obstacle the elements employed have a common typical character i e the consistency error can reach order o h 3 2 nearly 1 2 order higher than their interpolation error when the exact solution of the considered problem belongs to h 5 2 for any e 0 by making full use of special properties of the element s interpolations and bramble hilbert lemma the superconvergence error estimates of order o h 3 2 in the broken h1 norm are derived finally some numerical results are provided to confirm the theoretical results

nearly holomorphic sections on compact hermitian symmetric spaces abstract let x be a kahler manifold and e be a hermitian vector bundle on x we investigate the space n x e of nearly holomorphic sections in e which generalizes the notion of nearly holomorphic functions introduced by shimura if x u k is a compact hermitian symmetric space and e is u homogeneous it turns out that n x e coincides with the space of u finite vectors in c x e and we obtain new results on the u type decomposition of the hilbert space of square integrable sections as an application we determine this decomposition for the holomorphic tangent bundle of x

special set and solutions of coupled nonlinear schrodinger equations a special set of n coupled nonlinear schrodinger equations which consists of 2n interaction types each of which is characterized by a specific array of interaction parameters is presented it is shown that every lame function of order n n is a solution for one or more components for one or more interaction types of this special set simple rules that relate interaction and solution types and interesting features of these relationships are presented

a posteriori error estimates of discontinuous galerkin methods for the signorini problem a reliable and efficient a posteriori error estimator is derived for a class of discontinuous galerkin dg methods for the signorini problem a common property shared by many dg methods leads to a unified error analysis with the help of a constraint preserving enriching map the error estimator of dg methods is comparable with the error estimator of the conforming methods numerical experiments illustrate the performance of the error estimator

hua operators and poisson transform for bounded symmetric domains let be a bounded symmetric domain of non tube type in c n with rank r and s its shilov boundary we consider the poisson transform p s f z for a hyperfunction f on s defined by the poisson kernel p s z u h z z n r h z u n r 2 s z u s s c for all s satisfying certain non integral condition we find a necessary and sufficient condition for the functions in the image of the poisson transform in terms of hua operators when is the type i matrix domain in m n m c n less than or slanted equal to m we prove that an eigenvalue equation for the second order m n n valued hua operator characterizes the image 2006 elsevier inc all rights reserved

n coupled nonlinear schrodinger equations special set and applications to n 3 analytic solutions for a special set of n coupled nonlinear schrodinger equations characterized by 2n interaction types are presented for n 1 3 they provide an overview of the important role played by nonlinear couplings

jordan structures in harmonic functions and fourier algebras on homogeneous spaces we study the jordan structures and geometry of bounded matrix valued harmonic functions on a homogeneous space and their analogue the harmonic functionals in the setting of fourier algebras of homogeneous spaces

branching laws for discrete wallach points we consider the projective representations of the group of holomorphic automorphisms of a symmetric tube domain v i that are obtained by analytic continuation of the holomorphic discrete series for a representation corresponding to a discrete point in the wallach set we find the decomposition under restriction to the identity component of gl using riesz distributions an explicit intertwining operator is constructed as an analytic continuation of an integral operator the density of the plancherel measure involves quotients of functions and the c function for a symmetric cone of smaller rank

entire nonradial solutions for non cooperative coupled elliptic system with critical exponents in r3 abstract we consider the following coupled elliptic system s n u 1 u n 2 n 2 u 2 n 2 v n n 2 in r n v 2 v n 2 n 2 v 2 n 2 u n n 2 in r n u v 0 u v d 1 2 r n where n 3 1 2 are two positive constants and 0 is the coupling constant when n 3 we prove the existence of infinitely many positive nonradial solutions

higher order periodic solutions of coupled ϕ4 and ϕ6 models we obtain several higher order periodic solutions of i a coupled symmetric 4 model in an external field ii a coupled asymmetric 4 model iii a coupled symmetric asymmetric 4 model and iv a coupled 6 model in terms of lame polynomials and obtain the corresponding hyperbolic solutions in the appropriate limit all these solutions are unusual in the sense that while they are the solutions of the coupled problems they are not the solutions of the corresponding uncoupled problems possible physical applications of these solutions include periodic domain walls in magnetic and structural phase transitions as well as in field theory

a new error analysis for discontinuous finite element methods for linear elliptic problems the standard a priori error analysis of discontinuous galerkin methods requires additional regularity on the solution of the elliptic boundary value problem in order to justify the galerkin orthogonality and to handle the normal derivative on element interfaces that appear in the discrete energy norm in this paper a new error analysis of discontinuous galerkin methods is developed using only the h k weak formulation of a boundary value problem of order 2k this is accomplished by replacing the galerkin orthogonality with estimates borrowed from a posteriori error analysis and by using a discrete energy norm that is well defined for functions in h k

reproducing kernel functions and asymptotic expansions on jordan kepler manifolds abstract we study the complex geometry of generalized kepler manifolds defined in jordan theoretic terms introduce hilbert spaces of holomorphic functions defined by radial measures and find the complete asymptotic expansion of the corresponding reproducing kernels for kahler potentials both in the flat and bounded setting

a priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems we analyze three discontinuous galerkin approximations for solving elliptic problems in two or three dimensions in each one the basic bilinear form is nonsymmetric the first one has a penalty term on edges the second has one constraint per edge and the third is totally unconstrained for each of them we prove hp error estimates in the h1 norm optimal with respect to h the mesh size and nearly optimal with respect to p the degree of polynomial approximation we establish these results for general elements in two and three dimensions for the unconstrained method we establish a new approximation result valid on simplicial elements l2 estimates are also derived for the three methods

toeplitz c algebras on bounded symmetric domains in this paper we develop a structure theory for the toeplitz c algebra y for an arbitrary bounded symmetric domain d in c classical or exceptional as the main result it is shown that 5y is a c algebra of type i which is solvable i e admits a finite composition sequence of closed ideals sk in 7 such that the subquotients fk i k are continuous fields of elementary c algebras of compact operators the length of this composition sequence coincides with the rank r of d as a hermitian symmetric space for 0 k r the spectral components sk of ay parametrizing the irreducible representations of y are realized in terms of the boundary components complex analytic faces of d the structure theory for y is based on the fact that the tangent space z c c of d carries a jordan algebraic structure z is a jordan triple system with triple product uv w describing the geometry of d in algebraic terms for example d is the open unit ball with respect to the so called spectral norm on z and the boundary components of d are in 1 1 correspondence with the tripotents e e z partial isometries satisfying ee e 4 e in particular the shilov boundary s of d consists of all tripotents of maximal rank r the jordan theoretic description of d was used in 17 to determine an explicit peter weyl decomposition of the hardy space h2 s cf 15 in terms of the norm functions generalized determinants associated with the jordan triple

multiple bound states of nonlinear schrodinger systems this paper is concerned with existence of bound states for schrodinger systems which have appeared as several models from mathematical physics we establish multiplicity results of bound states for both small and large interactions this is done by different approaches depending upon the sizes of the interaction parameters in the systems for small interactions we give a new approach to deal with multiple bound states the novelty of our approach lies in establishing a certain type of invariant sets of the associated gradient flows for large interactions we use a minimax procedure to distinguish solutions by analyzing their morse indices

two level additive schwarz preconditioners for nonconforming finite element methods two level additive schwarz preconditioners are developed for the nonconforming p1 finite element approximation of scalar second order symmetric positive definite elliptic boundary value problems the morley finite element approximation of the biharmonic equation and the divergence free nonconforming p1 finite element approximation of the stationary stokes equations the condition numbers of the preconditioned systems are shown to be bounded independent of mesh sizes and the number of subdomains in the case of generous overlap

conforming and discontinuous galerkin fem in space for solving parabolic obstacle problem abstract in this article we propose and analyze conforming and discontinuous galerkin dg finite element methods for numerical approximation of the solution of the parabolic variational inequality associated with a general obstacle in r d d 2 3 for fully discrete conforming method we use globally continuous and piecewise linear finite element space whereas for the fully discrete dg scheme we employ piecewise linear finite element space for spatial discretization the time discretization has been done by using the implicit backward euler method we present the error analysis for the conforming and the dg fully discrete schemes and derive an error estimate of optimal order o h t in a certain energy norm defined precisely in the article the analysis is performed without any assumptions on the speed of propagation of the free boundary but only assumes the pragmatic regularity that u t l 2 0 t l 2 the obstacle constraints are incorporated at the lagrange nodes of the triangular mesh and the analysis exploits the lagrange interpolation we present some numerical experiment to illustrate the performance of the proposed methods

residual type a posteriori error estimates for elliptic obstacle problems a posteriori error estimators of residual type are derived for piecewise linear finite element approximations to elliptic obstacle problems an instrumental ingredient is a new interpolation operator which requires minimal regularity exhibits optimal approximation properties and preserves positivity both upper and lower bounds are proved and their optimality is explored with several examples sharp a priori bounds for the a posteriori estimators are given and extensions of the results to double obstacle problems are briefly discussed

complete monotonicity for inverse powers of some combinatorially defined polynomials we prove the complete monotonicity on 0 infty n for suitable inverse powers of the spanning tree polynomials of graphs and more generally of the basis generating polynomials of certain classes of matroids this generalizes a result of szeg and answers among other things a long standing question of lewy and askey concerning the positivity of taylor coefficients for certain rational functions our proofs are based on two ab initio methods for proving that p beta is completely monotone on a convex cone c the determinantal method and the quadratic form method these methods are closely connected with harmonic analysis on euclidean jordan algebras or equivalently on symmetric cones we furthermore have a variety of constructions that given such polynomials can create other ones with the same property among these are algebraic analogues of the matroid operations of deletion contraction direct sum parallel connection series connection and 2 sum the complete monotonicity of p beta for some beta 0 can be viewed as a strong quantitative version of the half plane property hurwitz stability for p and is also related to the rayleigh property for matroids

dixmier trace for toeplitz operators on symmetric domains abstract for toeplitz operators on bounded symmetric domains of higher rank there is no obvious way to define the dixmier trace within the toeplitz c algebra since commutators are in general not compact in this paper we solve this problem by constructing a hilbert quotient module corresponding to partitions of length 1 which leads to commutators in the macaev class l n we also obtain an explicit formula for the dixmier trace of such commutators in terms of the underlying boundary geometry which involves a new type of flag manifold defined in jordan theoretic terms

hp discontinuous galerkin methods for strongly nonlinear elliptic boundary value problems in this paper we have analyzed a one parameter family of hp discontinuous galerkin methods for strongly nonlinear elliptic boundary value problems nabla cdot rm a u nabla u f u nabla u 0 with dirichlet boundary conditions these methods depend on the values of the parameter theta in 1 1 where 1 corresponds to the nonsymmetric and 1 corresponds to the symmetric interior penalty methods when rm a u nabla u nabla u and f u u f that is for the poisson problem the error estimate in the broken h 1 norm which is optimal in h mesh size and suboptimal in p degree of approximation is derived using piecewise polynomials of degree p 2 when the solution u in h 5 2 omega in the case of linear elliptic problems also this estimate is optimal in h and suboptimal in p further optimal error estimate in the l 2 norm when 1 is derived numerical experiments are presented to illustrate the theoretical results

excitation threshold for the discrete coupled schrodinger lattice system this paper is concerned with the excitation threshold for the ground state in the coupled discrete nonlinear schrodinger lattice system excitation threshold is characterized by the variational methods we establish the existence of the excitation threshold connected with the dimensionality d of the lattice we prove that if d 2 then the excitation threshold exists and the ground state exists if and only if the total power is greater than the excitation threshold the compactness of the minimizing sequence follows by the concentration compactness principle we also prove the upper estimates on the excitation threshold and the frequency of the ground state

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

painleve analysis and integrability of coupled non linear schrodinger equations considering a system of coupled non linear schrodinger nls equations the authors discuss the integrability properties through painleve p analysis for the two coupled nls equations they show that there exists a pair of parametric values possessing the p property for which the associated backlund transformation bt and the hirota bilinearisation are constructed these parametric choices are identical to those of zakharov and schulman 1982 who established the integrability in terms of motion invariants finally they extend the p analysis to the n coupled nls system and identify two parametric choices possessing the p property which are natural generalisations of the two coupled nls cases

positive solutions to some systems of coupled nonlinear schrodinger equations abstract we study the existence of nontrivial bound state solutions to the following system of coupled nonlinear time independent schrodinger equations u j j u j j u j 3 k 1 k j n j k u j u k 2 u j w 1 2 r n j 1 n where n 1 2 3 j j 0 for j 1 n the coupling parameters j k k j r for j k 1 n j k precisely we prove the existence of nonnegative bound state solutions for suitable conditions on the coupling factors additionally with more restrictive conditions on the coupled parameters we show that the bound states founded are positive

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

the berezin transform and invariant differential operators the berezin calculus is important to quantum mechanics creation annihilation operators and operator theory toeplitz operators we study the basic berezin transform linking the contravariant and covariant symbol for all bounded symmetric domains and express it in terms of invariant differential operators

an a priori error analysis of the local discontinuous galerkin method for elliptic problems in this paper we present the first a priori error analysis for the local discontinuous galerkin ldg method for a model elliptic problem for arbitrary meshes with hanging nodes and elements of various shapes we show that for stabilization parameters of order one the l2 norm of the gradient and the l2 norm of the potential are of order k and k 1 2 respectively when polynomials of total degree at least k are used if stabilization parameters of order h 1 are taken the order of convergence of the potential increases to k 1 the optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

sharp thresholds of blow up and global existence for the coupled nonlinear schrodinger system in this paper we establish two new types of invariant sets for the coupled nonlinear schrodinger system in the euclidean n space rn and derive two sharp thresholds of blow up and global existence for its solutions some analogous results for the nonlinear schrodinger system posed on the hyperbolic space hn and on the standard 2 sphere s2 are also presented our arguments and constructions are improvements of some previous works on this direction at the end we give some heuristic analysis about the strong instability of the solitary waves the relation between the two types of thresholds is a very interesting problem and we leave it as an open problem for further study

discontinuous galerkin methods for solving elliptic variational inequalities we study discontinuous galerkin methods for solving elliptic variational inequalities of both the first and second kinds analysis of numerous discontinuous galerkin schemes for elliptic boundary value problems is extended to the variational inequalities we establish a priori error estimates for the discontinuous galerkin methods which reach optimal order for linear elements results from some numerical examples are reported

a posteriori error control of discontinuous galerkin methods for elliptic obstacle problems in this article we derive an a posteriori error estimator for various discontinuous galerkin dg methods that are proposed in wang han and cheng siam j numer anal 48 708 733 2010 for an elliptic obstacle problem using a key property of dg methods we perform the analysis in a general framework the error estimator we have obtained for dg methods is comparable with the estimator for the conforming galerkin cg finite element method in the analysis we construct a non linear smoothing function mapping dg finite element space to cg finite element space and use it as a key tool the error estimator consists of a discrete lagrange multiplier associated with the obstacle constraint it is shown for non over penalized dg methods that the discrete lagrange multiplier is uniformly stable on non uniform meshes finally numerical results demonstrating the performance of the error estimator are presented

adaptive discontinuous galerkin methods for solving an incompressible stokes flow problem with slip boundary condition of frictional type abstract we consider the numerical solution of a variational inequality arising in the study of an incompressible stokes flow with a nonlinear slip boundary condition of frictional type we study several discontinuous galerkin dg schemes for solving the problem and derive reliable and efficient residual type a posteriori error estimators an adaptive dg method is constructed based on the error estimators to solve the problem some numerical examples are presented to illustrate the efficiency of the adaptive dg method

solitary and self similar solutions of two component system of nonlinear schrodinger equations conventionally to learn wave collapse and optical turbulence one must study finite time blow up solutions of one component self focusing nonlinear schrodinger equations nlse here we consider simultaneous blow up solutions of two component systems of self focusing nlse by studying the associated self similar solutions we prove two components of solutions blow up at the same time these self similar solutions may come from solitary wave solutions with multi bumps forming abundant geometric patterns which cannot be found in one component self focusing nlse our results may provide the first step to investigate optical turbulence in two component systems of nlse

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

a posteriori error analysis for a class of integral equations and variational inequalities we consider elliptic and parabolic variational equations and inequalities governed by integro differential operators of order 2s in 0 2 our main motivation is the pricing of european or american options under levy processes in particular pure jump processes or jump diffusion processes with tempered stable processes the problem is discretized using piecewise linear finite elements in space and the implicit euler method in time we construct a residual type a posteriori error estimator which gives a computable upper bound for the actual error in h s norm the estimator is localized in the sense that the residuals are restricted to the discrete non contact region numerical experiments illustrate the accuracy of the space and time estimators and show that they can be used to measure local errors and drive adaptive algorithms

a convergent adaptive algorithm for poisson s equation we construct a converging adaptive algorithm for linear elements applied to poisson s equation in two space dimensions starting from a macro triangulation we describe how to construct an initial triangulation from a priori information then we use a posteriors error estimators to get a sequence of refined triangulation and approximate solutions it is proved that the error measured in the energy norm decreases at a constant rate in each step until a prescribed error bound is reached extension to higher order elements in two space dimension and numerical results are included

convergence analysis of a conforming adaptive finite element method for an obstacle problem the adaptive algorithm for the obstacle problem presented in this paper relies on the jump residual contributions of a standard explicit residual based a posteriori error estimator each cycle of the adaptive loop consists of the steps solve estimate mark and refine the techniques from the unrestricted variational problem are modified for the convergence analysis to overcome the lack of galerkin orthogonality we establish r linear convergence of the part of the energy above its minimal value if there is appropriate control of the data oscillations surprisingly the adaptive mesh refinement algorithm is the same as in the unconstrained case of a linear pde in fact there is no modification near the discrete free boundary necessary for r linear convergence the arguments are presented for a model obstacle problem with an affine obstacle and homogeneous dirichlet boundary conditions the proof of the discrete local efficiency is more involved than in the unconstrained case numerical results are given to illustrate the performance of the error estimator

a posteriori error estimators for obstacle problems another look we show that a posteriori estimators for the obstacle problem are easily obtained from the theory for linear equations the theory would be even simpler if the lagrange multiplier does not have a nonconforming contribution as it has in actual finite element computations

efficient and reliable a posteriori error estimators for elliptic obstacle problems a posteriori error estimators are derived for linear finite element approximations to elliptic obstacle problems these estimators yield global upper and local lower bounds for the discretization error here discretization error means the sum of two contributions the distance between continuous and discrete solution in the energy norm and some quantity that is related to the distance of continuous and discrete contact set moreover the local error indicators in the interior of the discrete contact set reduce to quantities that measure only data resolution

function spaces and reproducing kernels on bounded symmetric domains there are several natural hilbert spaces of holomorphic functions on a bounded symmetric domain such are the bergman type spaces on which the holomorphic discrete series operates and the hardy type spaces which are related to the analytic continuation of the holomorphic discrete series also closely related is the bergmann space of entire functions on the ambient which arises as the closure of the polynomials with respect to a natural inner product the space of holomorphic polynomials decomposes into irreducible subspaces under the action of the isotropy group k of the domain the main facts about this decomposition were proved by schmid 21 for another proof see 22 each irreducible subspace contains a unique normalized l invariant spherical polynomial where l is the isotropy group of the shilov boundary in k our first main result is the explicit computation of the norms of the spherical polynomials with respect to each of the hilbert spaces considered for the domains of classical type they were considered by hua 9 and for some of the hilbert spaces this was done before by upmeier 24 using different methods for certain others there are partial results in 22 we are able to do this in a fairly simple unified way by making strong use of gindikin s generalized gamma function s next we obtain a description of the reproducing kernels of the k irreducible subspaces in each of our hilbert spaces and an expansion in terms of these for

note on ground states of a nonlinear schrodinger system abstract we give a sufficient condition for the existence of positive radial ground states of the time independent schrodinger system u 1 u 1 1 u 1 3 12 u 2 2 u 1 13 u 3 2 u 1 in r n u 2 u 2 12 u 1 2 u 2 2 u 2 3 23 u 3 2 u 2 in r n u 3 u 3 13 u 1 2 u 3 23 u 2 2 u 3 3 u 3 3 in r n u 1 x 0 u 2 x 0 u 3 x 0 as x where n 1 2 3 0 j 0 and i j 0 i j for i j 1 2 3 and in some special cases our conditions are also necessary

a posteriori error estimation and adaptive mesh refinement techniques abstract we analyse three different a posteriori error estimators for elliptic partial differential equations they are based on the evaluation of local residuals with respect to the strong form of the differential equation on the solution of local problems with neumann boundary conditions and on the solution of local problems with dirichlet boundary conditions we prove that all three are equivalent and yield global upper and local lower bounds for the true error thus adaptive mesh refinement techniques based on these estimators are capable to detect local singularities of the solution and to appropriately refine the grid near these singularities some numerical examples prove the efficiency of the error estimators and the mesh refinement techniques