on the spaces lp x ω and wm p x ω in this paper we present some basic results on the generalized lebesgue spaces l p x omega and generalized lebesgue sobolev spaces w m w p x omega these results provide the necessary framework for the study of variational problems and elliptic equations with non standard p x growth conditions c 2001 academic press

boundary trace embedding theorems for variable exponent sobolev spaces we study boundary trace embedding theorems for variable exponent sobolev space w1 p let be an open bounded or unbounded domain in rn satisfying strong local lipschitz condition under the hypotheses that p l 1 infp x supp x n we prove that there is a continuous boundary trace embedding w1 p lq provided q a measurable function on satisfies condition p x q x n 1 p x n p x for x

low density parity check codes based on finite geometries a rediscovery and new results this paper presents a geometric approach to the construction of low density parity check ldpc codes four classes of ldpc codes are constructed based on the lines and points of euclidean and projective geometries over finite fields codes of these four classes have good minimum distances and their tanner 1981 graphs have girth 6 finite geometry ldpc codes can be decoded in various ways ranging from low to high decoding complexity and from reasonably good to very good performance they perform very well with iterative decoding furthermore they can be put in either cyclic or quasi cyclic form consequently their encoding can be achieved in linear time and implemented with simple feedback shift registers this advantage is not shared by other ldpc codes in general and is important in practice finite geometry ldpc codes can be extended and shortened in various ways to obtain other good ldpc codes several techniques of extension and shortening are presented long extended finite geometry ldpc codes have been constructed and they achieve a performance only a few tenths of a decibel away from the shannon theoretical limit with iterative decoding

multigrid solution of the two dimensional euler equations on unstructured triangular meshes a multigrid algorithm has been developed to accelerate the convergence of the euler equations to a steady state on unstructured triangular meshes the method operates on a sequence of coarse and fine unstructured meshes and assumes no relation exists between the various meshes a tree search algorithm is used to efficiently identify regions of overlap between coarse and fine grid cells the multigrid method is applied to two different discretizations of the euler equations and results about multi element airfoils are presented for both discretization schemes convergence is accelerated by an order of magnitude resulting in convergence rates comparable to those obtained with structured multigrid algorithms

prismatic grid generation for three dimensional complex geometries the paper describes generation of semiunstructu red prismatic grids for three dimensional complex geometries a new method of generation is presented which couples both algebraic and elliptic steps this combination yields low computation cost as well as smoothness of the grid main advantages of the developed grid generator are its direct control of grid orthogonality and spacing as well as its generality for treatment of three dimensional geometries the method marches a surface consisting of triangular faces away from the body surface employment of prismatic elements is a relatively new approach toward three dimensional complex geometry numerical simulations of viscous flows a body surface is covered with triangles which gives the geometric flexibility whereas the structure of the mesh in the direction normal to the surface provides better resolution of the viscous regions an f 16a aircraft geometry was included in the applications to investigate efficiency and to demonstrate robustness of the method in handling relatively complex topologies grid generation time for the entire aircraft domain was of the order of minutes on a workstation

on the second solution to a critical growth robin problem abstract we investigate the existence of the second mountain pass solution to a robin problem where the equation is at critical growth and depends on a positive parameter more precisely we determine existence and nonexistence regions for this type of solutions depending both on and on the parameter in the boundary conditions

strand grid solution procedures for sharp corners the strand cartesian grid approach provides many advantages for complex moving body flow simulations including fully automatic volume grid generation highly scalable domain connectivity and high order accuracy in this work the authors evaluate methods of handling sharp corners with strand grids through combinations of strand vector smoothing multiple strands emanating from a single surface node and telescoping cartesian refinement into corner regions of the near body grid a new discretization strategy is introduced to better tolerate mesh skewness induced by strand smoothing these approaches are tested for unsteady laminar and high reynolds number turbulent flows for standard viscous high aspect ratio grids smoothed strands with telescoping cartesian refinement provide the most accurate results with the least complexity mesh discontinuities associated with the use of multiple strands at sharp corners produce more error than with smoothed strands with both strand approaches vector smoothing

elliptic boundary value problems with nonstandard growth conditions abstract we study different boundary value problems to the p x laplacean equation namely of robin and signorini types we prove the existence and uniqueness of weak solutions to the problems under study and also their continuous dependence on the exponent data

existence and multiplicity of solutions for quasilinear nonhomogeneous problems an orlicz sobolev space setting abstract we study the boundary value problem div log 1 u q u p 2 u f u in u 0 on where is a bounded domain in r n with smooth boundary we distinguish the cases where either f u u p 2 u u r 2 u or f u u p 2 u u r 2 u with p q 1 p q min n r and r n p n p n p in the first case we show the existence of infinitely many weak solutions for any 0 in the second case we prove the existence of a nontrivial weak solution if is sufficiently large our approach relies on adequate variational methods in orlicz sobolev spaces

average stopping set weight distributions of redundant random ensembles in this paper redundant random ensembles are defined and their average stopping set ss weight distributions are analyzed a redundant random ensemble consists of a set of binary matrices with linearly dependent rows these linearly dependent rows significantly reduce the number of stopping sets ss of small size upper and lower bounds on the average ss weight distribution of the redundant random ensembles are proved based on a combinatorial argument asymptotic forms of these bounds reveal asymptotic behavior of the average ss weight distributions from these bounds a tradeoff between the number of redundant rows corresponding to decoding complexity of belief propagation on binary erasure channel and the average ss weight distribution corresponding to decoding performance can be derived

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

on ensembles of low density parity check codes asymptotic distance distributions we derive expressions for the average distance distributions in several ensembles of regular low density parity check codes ldpc among these ensembles are the standard one defined by matrices having given column and row sums ensembles defined by matrices with given column sums or given row sums and an ensemble defined by bipartite graphs

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

existence and non existence results for a quasilinear problem with nonlinear boundary condition abstract we study the problem div a x u p 2 u 1 x 1 u q 2 u h x u r 2 u in r n a x u p 2 u n b x u p 2 u g x u on u 0 in where is an unbounded domain with smooth boundary n denotes the unit outward normal vector on and 0 are real parameters we assume throughout that p q r p pn n p 1 p n n 1 q n p p n while a b and h are positive functions we show that there exist an open interval i and 0 such that the problem has no solution if i and 0 furthermore there exist an open interval j i and 0 0 such that for any j the above problem has at least a solution if 0 but it has no solution provided that 0 0 our paper extends previous results obtained by j chabrowski and k pfluger

stopping sets of algebraic geometry codes stopping sets and stopping set distribution of a linear code play an important role in the performance analysis of iterative decoding for this linear code let c be an n k linear code over fq with parity check matrix h where the rows of h may be dependent let n 1 2 n denote the set of column indices of h a stopping set s of c with parity check matrix h is a subset of n such that the restriction of h to s does not contain a row of weight 1 the stopping set distribution ti h i 0n enumerates the number of stopping sets with size i of c with parity check matrix h denote h the parity check matrix consisting of all the nonzero codewords in the dual code c in this paper we study stopping sets and stopping set distributions of some residue algebraic geometry ag codes with parity check matrix h first we give two descriptions of stopping sets of residue ag codes for the simplest ag codes i e the generalized reed solomon codes it is easy to determine all the stopping sets then we consider the ag codes from elliptic curves we use the group structure of rational points of elliptic curves to present a complete characterization of stopping sets then the stopping sets the stopping set distribution and the stopping distance of the ag code from an elliptic curve are reduced to the search counting and decision versions of the subset sum problem in the group of rational points of the elliptic curve respectively finally for some special cases we determine the stopping set distributions of the ag codes from elliptic curves

high order flux correction finite difference schemes for strand grids a novel high order method combining unstructured flux correction along body surfaces and high order finite differences normal to surfaces is formulated for unsteady viscous flows on strand grids the flux correction algorithm is applied in each unstructured layer of the strand grid and the layers are then coupled together via a source term containing derivatives in the strand direction strand direction derivatives are approximated to high order via summation by parts operators for first derivatives and second derivatives with variable coefficients we show how this procedure allows for the proper truncation error canceling properties required for the flux correction scheme the resulting scheme possesses third order design accuracy but often exhibits fourth order accuracy when higher order derivatives are employed in the strand direction especially for highly viscous flows we prove discrete conservation for the new scheme and time stability in the absence of the flux correction terms results in two dimensions are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second order algorithms

existence and multiplicity of solutions for a neumann problem involving the p x laplace operator abstract in this paper we study the following nonlinear neumann boundary value problem div u p x 2 u u p x 2 u f x u x t r u v 0 x t r where r n is a bounded domain with smooth boundary u v is the outer unit normal derivative on 0 is a real number p is a continuous function on with inf x p x 1 f r r is a continuous function using the three critical point theorem due to ricceri under the appropriate assumptions on f we establish the existence of at least three solutions of this problem some known results are generalized

distance distributions in ensembles of irregular low density parity check codes we derive asymptotic expressions for the average distance distributions in ensembles of irregular low density parity check ldpc codes the ensembles are defined by matrices with given profiles of column and row sums

improved upper bounds on stopping redundancy for a linear block code with minimum distance d its stopping redundancy is the minimum number of check nodes in a tanner graph representation of the code such that all nonempty stopping sets have size d or larger we derive new upper bounds on stopping redundancy for all linear codes in general and for maximum distance separable mds codes specifically and show how they improve upon previous results for mds codes the new bounds are found by upper bounding the stopping redundancy by a combinatorial quantity closely related to turan numbers the turan number t v k t is the smallest number of t subsets of a v set such that every k subset of the v set contains at least one of the t subsets asymptotically we show that the stopping redundancy of mds codes with length n and minimum distance d 1 is t n d 1 d 2 1 o n 1 for fixed d and is at most t n d 1 d 2 3 o n 1 for fixed code dimension k n d 1 for d 3 4 we prove that the stopping redundancy of mds codes is equal to t n d 1 d 2 for which exact formulas are known for d 5 we show that the stopping redundancy of mds codes is either t n 4 3 or t n 4 3 1

nonexistence existence and multiplicity of positive solutions to the p x laplacian nonlinear neumann boundary value problem abstract we study the nonexistence existence and multiplicity of positive solutions for the nonlinear neumann boundary value problem involving the p x laplacian of the form p x u u p x 2 u f x u in u p x 2 u g x u on where is a bounded smooth domain in r n p c 1 and p x 1 for x using the sub supersolution method and the variational principles under appropriate assumptions on f and g we prove that there exists 0 such that the problem has at least two positive solutions if has at least one positive solution if and has no positive solution if

feature driven cartesian adaptive mesh refinement for vortex dominated flows we develop locally normalized feature detection methods to guide the adaptive mesh refinement amr process for cartesian grid systems to improve the resolution of vortical features in aerodynamic wakes the methods include the q criterion 1 the l 2 method 2 the l c i method 3 and the l method 4 specific attention is given to automate the feature identification process by applying a local normalization based upon the shear strain rate so that they can be applied to a wide range of flow fields without the need for user intervention to validate the methods we assess tagging efficiency and accuracy using a series of static vortex dominated flow fields and use the methods to drive the amr process for several theoretical and practical simulations we demonstrate that the adaptive solutions provide comparable accuracy to solutions obtained on uniformly refined meshes at a fraction of the computational cost overall the normalized feature detection methods are shown to be effective in driving the amr process in an automated and efficient manner

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

asymptotic enumeration methods for analyzing ldpc codes we show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low density parity check ldpc codes in particular we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular ldpc code ensembles we then consider the binary erasure channel bec using these estimates we derive lower bounds on the error exponent under iterative decoding of ldpc codes used over the bec both regular and irregular code structures are considered these bounds are compared to the corresponding bounds when optimal maximum likelihood ml decoding is applied

interaction between the geometry of the boundary and positive solutions of a semilinear neumann problem with critical nonlinearity abstract we consider the problem u u un 2 n 2 u 0 in u v 0 on where is a bounded smooth domain in r n n 3 we show that for large least energy solutions of the above problem have a unique maximum point p on and the limit points of p as are contained in the set of the points of maximum mean curvature we also prove that if has k peaks then the equation has at least k solutions for large

infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous neumann conditions abstract the aim of this paper is to establish the existence of an unbounded sequence of weak solutions for a class of differential equations with p x laplacian and subject to small perturbations of nonhomogeneous neumann conditions the approach is based on variational methods

tree structure expectation propagation for ldpc decoding over the bec we present the tree structure expectation propagation tree ep algorithm to decode low density parity check ldpc codes over discrete memoryless channels dmcs expectation propagation generalizes belief propagation bp in two ways first it can be used with any exponential family distribution over the cliques in the graph second it can impose additional constraints on the marginal distributions we use this second property to impose pairwise marginal constraints over pairs of variables connected to a check node of the ldpc code s tanner graph thanks to these additional constraints the tree ep marginal estimates for each variable in the graph are more accurate than those provided by bp we also reformulate the tree ep algorithm for the binary erasure channel bec as a peeling type algorithm tep and we show that the algorithm has the same computational complexity as bp and it decodes a higher fraction of errors we describe the tep decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters the solution of these equations is used to predict the tep decoder performance in both the asymptotic regime and the finite length regimes over the bec while the asymptotic threshold of the tep decoder is the same as the bp decoder for regular and optimized codes we propose a scaling law for finite length ldpc codes which accurately approximates the tep improved performance and facilitates its optimization

finite length analysis of low density parity check codes on the binary erasure channel in this paper we are concerned with the finite length analysis of low density parity check ldpc codes when used over the binary erasure channel bec the main result is an expression for the exact average bit and block erasure probability for a given regular ensemble of ldpc codes when decoded iteratively we also give expressions for upper bounds on the average bit and block erasure probability for regular ldpc ensembles and the standard random ensemble under maximum likelihood ml decoding finally we present what we consider to be the most important open problems in this area

solutions for neumann boundary value problems involving p x laplace operators abstract in this paper we study the nonlinear neumann boundary value problem of the following form p div u p x 2 u u p x 2 u f x u in u p x 2 u g x u on using the variational method under appropriate assumptions on f and g we obtain a number of results on existence and multiplicity of solutions also what is also interesting is that we obtain some results which can be considered as extensions of the classical result named combined effects of concave and convex nonlinearities moreover the positive solution of the problem is considered

further study on the effect of boundary conditions abstract this paper concerns the least energy solutions to a semilinear elliptic equation the role of geometry of the boundary is studied when a parameter in the boundary condition tends to a critical index as well as to infinity

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

on the stopping distance and the stopping redundancy of codes it is now well known that the performance of a linear code copf under iterative decoding on a binary erasure channel and other channels is determined by the size of the smallest stopping set in the tanner graph for copf several recent papers refer to this parameter as the stopping distance s of copf this is somewhat of a misnomer since the size of the smallest stopping set in the tanner graph for copf depends on the corresponding choice of a parity check matrix it is easy to see that s les d where d is the minimum hamming distance of copf and we show that it is always possible to choose a parity check matrix for copf with sufficiently many dependent rows such that s d we thus introduce a new parameter the stopping redundancy of copf defined as the minimum number of rows in a parity check matrix h for copf such that the corresponding stopping distance s h attains its largest possible value namely s h d we then derive general bounds on the stopping redundancy of linear codes we also examine several simple ways of constructing codes from other codes and study the effect of these constructions on the stopping redundancy specifically for the family of binary reed muller codes of all orders we prove that their stopping redundancy is at most a constant times their conventional redundancy we show that the stopping redundancies of the binary and ternary extended golay codes are at most 34 and 22 respectively finally we provide upper and lower bounds on the stopping redundancy of mds codes

regularity and existence of solutions of elliptic equations with p q growth conditions for some positive constants m a4 and for exponents q 2 p 2 2 under 1 2 1 3 and some other assumptions by assuming also that the quotient q p is sufficiently close to one in dependence on n precisely if q p c n n 2 then we prove that every weak solution to 1 1 of class 4 4 0 is locally lipschitz continuous in q moreover there are positive constants 8 c and 0 2 1 such that

positive solutions for robin problem involving the p x laplacian abstract consider robin problem involving the p x laplacian on a smooth bounded domain as follows p x u f x u in u p x 2 u u p x 2 u 0 on applying the sub supersolution method and the variational method under appropriate assumptions on f we prove that there exists 0 such that the problem has at least two positive solutions if 0 has at least one positive solution if and has no positive solution if to prove the results we prove a norm on w 1 p x without the part of l p x which is equivalent to usual one and establish a special strong comparison principle for robin problem

stopping set distributions of some reed muller codes stopping sets and stopping set distribution of a linear code are used to determine the performance of this code under iterative decoding over a binary erasure channel bec let c be a binary n k linear code with parity check matrix h where the rows of h may be dependent a stopping set s of c with parity check matrix h is a subset of column indices of h such that the restriction of h to s does not contain a row of weight one the stopping set distribution ti h i 0n enumerates the number of stopping sets with size i of c with parity check matrix h note that stopping sets and stopping set distribution are related to the parity check matrix h of c let h be the parity check matrix of c which is formed by all the nonzero codewords of its dual code c a parity check matrix h is called bec optimal if ti h ti h i 0 1 n and h has the smallest number of rows in this paper we study stopping sets stopping set distributions and bec optimal parity check matrices of binary linear codes using finite geometry in combinatorics we obtain bec optimal parity check matrices and then determine the stopping set distributions for the simplex codes the hamming codes the first order reed muller codes and the extended hamming codes which are some reed muller codes or their shortening or puncturing versions

infinitely many positive solutions for a p x kirchhoff type equation this paper is concerned with the existence of infinitely many positive solutions to a class of p x kirchhoff type problem by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish the existence of infinitely many distinct positive solutions whose w1 p x norms and l norms tend to zero under suitable hypotheses about nonlinearity

existence results to elliptic systems with nonstandard growth conditions abstract nonstandard growth conditions in partial differential equations have been the subject of recent developments in elastic mechanics and electrorheological fluid dynamics lecture notes in mathematics vol 1748 2000 c r acad sci paris ser i math 329 1999 393 398 math ussr izv 29 1987 33 66 in this work elliptic systems with nonstandard growth conditions are studied existence and multiplicity results under growth conditions on the reaction terms are established

average coset weight distribution of combined ldpc matrix ensembles in this paper the average coset weight distribution acwd of structured ensembles of low density parity check ldpc matrices which are called combined ensembles is discussed a combined ensemble is composed of a set of simpler ensembles such as a regular bipartite ensemble two classes of combined ensembles have prime importance a stacked ensemble and a concatenated ensemble the acwd formulas of these ensembles are shown in this paper such formulas play a key role to evaluate the average weight distribution of some classes of combined ensembles

existence results for the p laplacian with nonlinear boundary conditions in this paper we study the existence of nontrivial solutions for the problem pu u p 2u in a bounded smooth domain rn with a nonlinear boundary condition given by u p 2 u f u on the boundary of the domain the proofs are based on variational and topological arguments

solutions for p x laplacian dirichlet problems with singular coefficients using the critical point theory we investigate the existence and multiplicity of solutions for p x laplacian dirichlet problem with singular coefficients

on existence and multiplicity of solutions of neumann boundary value problems for quasi linear elliptic equations abstract in the present paper the following neumann boundary value problem involving the p laplacian 1 1 p u f x u in u n 0 on is studied and some new existence and multiplicity results of solutions for the problem 1 1 are obtained

analysis of message passing decoding of finite length concatenated codes we analyze the performance of message passing decoding of finite length concatenated codes we first show that the message passing decoder is closely related to a dual optimization decoder the connections between these two decoders are further elucidated by proving that both of them attain the same objective function value of a generalized linear programming decoder in the limit as the signal to noise ratio snr goes to infinity consequently the framework of pseudo weight analysis which was originally proposed for analyzing the linear programming decoder can be extended to analyze the performance of the message passing decoder for finite length codes we then derive lower bounds to the pseudo weights of general concatenated codes by utilizing the special structure of their parity check matrices we finally present a method to increase the max fractional weight by adding redundant parity check constraints and thereby improving the decoding performance simulation studies are carried out to assess the performance of the proposed algorithms and substantiate the theoretic claims

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

on parity check collections for iterative erasure decoding that correct all correctable erasure patterns of a given size recently there has been interest in the construction of small parity check sets for iterative decoding of the hamming code with the property that each uncorrectable or stopping set of size three is the support of a codeword and hence uncorrectable anyway here we reformulate and generalize the problem and improve on this construction we show that a parity check collection that corrects all correctable erasure patterns of size m for the hamming code with codimension r provides in fact for all codes of codimension r a corresponding generic parity check collection with this property this leads in a natural way to a necessary and sufficient condition for such generic parity check collections we use this condition to construct a generic parity check collection for codes of codimension r correcting all correctable erasure patterns of size at most m for all r and mlesr thus generalizing the known construction for m 3 then we discuss optimality of our construction and show that it can be improved for mges3 and r large enough finally we discuss some directions for further research

stopping set elimination by parity check matrix extension via integer linear programming error rate floor phenomenon is known to be a serious impediment to the use of low density parity check ldpc codes for some practical applications that demand high data reliability in the case of binary erasure channels becs certain error prone patterns known as stopping sets are proven to cause this performance degradation a possible approach to diminish this drawback over becs is to eliminate stopping sets by parity check matrix extension given a parity check matrix h and a list mathcal l of its stopping sets we present an integer linear programming ilp formulation to find a parity check equation which eliminates the maximum number of stopping sets in mathcal l one of the distinguishing advantages of the proposed scheme is its flexibility for modifications such as limiting the weight of the new parity check row making the new row redundant or linearly independent 4 cycle avoidance and taking into account the sizes of stopping sets armed with these adjustments the method can provide good performance improvements as evidenced by simulation results furthermore for a given varrho in mathbb n by extending the basic formulation we provide an ilp formulation for finding a set of size varrho of parity check equations which can best eliminate the stopping sets in mathcal l among all such sets

existence and blow up rate of large solutions of p x laplacian equations with gradient terms abstract in this paper we investigate boundary blow up solutions of the problem p x u f x u k x u m x in u x as d x 0 where p x u div u p x 2 u is called the p x laplacian our results extend the previous work 25 of y liang q h zhang and c s zhao from the radial case to the non radial setting and 46 due to q h zhang and d motreanu from the assumption that k x u x m x is a small perturbation to the case in which k x u m x is a large perturbation we provide an exact estimate of the pointwise different behavior of the solutions near the boundary in terms of d x and in terms of the growth of the exponents furthermore the comparison principle is no longer applicable in our context since f x is not assumed to be monotone in this paper

compact imbeddings between variable exponent spaces with unbounded underlying domain abstract in this paper we have established some compact imbedding theorems for some subspaces of w 1 p x u when the underlying domain u is unbounded the domain we consider is mainly of type r n n 2 or r l l 2 where r m is a bounded domain with smooth boundary

density of smooth functions in wk p x ω kovacik rakosnik investigated the spaces l p x omega of functions which are integrable with variable power p x and the corresponding counterparts of the sobolev spaces w k p x omega we continue that investigation and describe a class of functions p x for which the set of smooth functions on omega is dense in w k p x omega as a corollary we obtain in terms of the distance function a condition on elements of w k p x omega sufficient to ensure that they belong to w 0 k p x omega

a folding unfolding algorithm for the construction of semi structured layers in hybrid grid generation abstract a method is presented for generating semi structured layers in hybrid grids suitable for high reynolds number flow simulations it can produce superior quality grids around convex and concave ridges of the domain compared to a standard prismatic or advancing layers generator in a first step hybrid quadrilateral triangular grids are employed to cluster the surface grid towards sharp corners and ridges starting from this surface grid as an initial front for the volume grid generation a prismatic and hexahedral layers generation technique is used containing degenerate faces to add or remove elements in convex or concave areas of the geometry respectively the method can automatically create structured like grids in concave gaps and better discretize the space around convex ridges to improve overall accuracy the final grid remains conforming to not complicate the solver and post processing requirements several examples illustrate the application of the method

existence of multiple positive solutions for inhomogeneous neumann problem in this paper we study the existence and nonexistence of multiple positive solutions for the inhomogeneous neumann boundary value problem u up u 0 withd u x under some assumptions on the boundary and the function x for x 0 x 0 x c it is shown that there exists a constant 0 such that problem possesses at least two positive solutions if and at least one positive solution if furthermore there are no positive solutions for problem if

the neumann boundary value problem of higher order quasilinear elliptic equation abstract this paper is concerned with the generalized solution to the neumann boundary value problem of higher order quasilinear elliptic equation 1 m 1 d a x m u f x u x b x m u g x u x we show that there exists at least one non trivial solution for the above problem in w m p x

existence of solutions for p x laplacian problems on a bounded domain in this paper we study the following p x laplacian problem div a x vd uv p x 2 d u b x v uv p x 2 u f x u x e u u 0 on p u where 1 p 1 l p x l p 2 n u s r n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in w 0 1 p x for the p x laplacian problems in the superlinear and sublinear cases 2004 elsevier inc all rights reserved