semigroup structural form for bernstein type operators and its applications in this note we provide a semigroup viewpoint for bernstein type operators a main ingredient of our approach is to obtain some explicit semigroup representation formulae which as simple forms are proposed for the fist time as direct applications we improve the corresponding results of de la cal and luquin 1992 1994 moreover some kinds of voronovskaja type results are made by using general semigroup expansion in the end we discuss corresponding generalizations of integral operators with some examples of hybrid durrmeyer type operators

gradient estimates in orlicz space for nonlinear elliptic equations abstract in this paper we generalize gradient estimates in l p space to orlicz space for weak solutions of elliptic equations of p laplacian type with small bmo coefficients in reifenberg flat domains our results improve the known results for such equations using a harmonic analysis free technique

multiple solutions for a class of p x laplacian equations in involving the critical exponent in this paper we first establish a principle of concentration compactness in then based on this concentration compactness principle we study the existence of solutions for a class of p x lapl

weak quasi symmetric functions rota baxter algebras and hopf algebras abstract we introduce the hopf algebra of quasi symmetric functions with semigroup exponents generalizing the hopf algebra qsym of quasi symmetric functions as a special case we obtain the hopf algebra qsym n of weak quasi symmetric functions which provides a framework for the study of a question proposed by g c rota relating symmetric type functions and rota baxter algebras we provide the transformation formulas between the weak monomial and fundamental quasi symmetric functions which extends the corresponding results for quasi symmetric functions moreover we show that qsym is a hopf subalgebra and a hopf quotient algebra of qsym n rota s question is addressed by identifying qsym n with the free commutative unitary rota baxter algebra x of weight 1 on one generator x which also allows us to equip x with a hopf algebra structure

twisted descent algebras and the solomon tits algebra abstract the notion of descent algebra of a bialgebra is lifted to the barratt joyal setting of twisted bialgebras the new twisted descent algebras share many properties with their classical counterparts for example there are twisted analogs of classical lie idempotents and of the peak algebra moreover the universal twisted descent algebra is equipped with two products and a coproduct and there is a fundamental rule linking all three this algebra is shown to be naturally related to the geometry of the coxeter complex of type a

on posets and hopf algebras abstract we generalize the notion of the rank generating function of a graded poset namely by enumerating different chains in a poset we can assign a quasi symmetric function to the poset this map is a hopf algebra homomorphism between the reduced incidence hopf algebra of posets and the hopf algebra of quasi symmetric functions this work implies that the zeta polynomial of a poset may be viewed in terms hopf algebras in the last sections of the paper we generalize the reduced incidence hopf algebra of posets to the hopf algebra of hierarchical simplicial complexes

sobolev embeddings in metric measure spaces with variable dimension in this article we study metric measure spaces with variable dimension we consider lebesgue spaces on these sets and embeddings of the riesz potential in these spaces we also investigate hajlasz type sobolev spaces and prove sobolev and trudinger inequalities with optimal exponents all of these questions lead naturally to function spaces with variable exponents

eulerian quasisymmetric functions we introduce a family of quasisymmetric functions called eulerian quasisymmetric functions which specialize to enu merators for the joint distribution of the permutation statistics major index and excedance number on permutations of fixed cycle type this family is analogous to a family of quasisymmetric func tions that gessel and reutenauer used to study the joint distribu tion of major index and descent number on permutations of fixed cycle type our central result is a formula for the generating func tion for the eulerian quasisymmetric functions which specializes to a new and surprising q analog of a classical formula of euler for the exponential generating function of the eulerian polynomials this q analog computes the joint distribution of excedance number and major index the only of the four important euler mahonian distributions that had not yet been computed our study of the eulerian quasisymmetric functions also yields results that include the descent statistic and refine results of gessel and reutenauer we also obtain q analogs q p analogs and quasisymmetric func tion analogs of classical results on the symmetry and unimodality of the eulerian polynomials our eulerian quasisymmetric functions refine symmetric functions that have occurred in various represen tation theoretic and enumerative contexts including macmahon s study of multiset derangements work of procesi and stanley on toric varieties of coxeter complexes stanley s work on chromatic symmetric functions and the work of the authors on the homology of a certain poset introduced by bjorner and welker

renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and l1 data abstract in this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and l 1 data and moreover we obtain the equivalence of renormalized solutions and entropy solutions

global weighted lorentz estimates to nonlinear parabolic equations over nonsmooth domains abstract an elaborate method is developed to establish a global calderon zygmund type theory in weighted lorentz spaces l q t for zero cauchy dirichlet problem of nonlinear parabolic equations of p laplacian type with p 2 d d 2 here we assume that the nonlinearity a a t x is merely measurable in the time variable t and has a mall bmo semi norm in the spatial variables x uniformly in variables while the boundary of bounded domain is flat in the sense of reifenberg our result not only develops nonlinear calderon zygmund theory under weak regularity assumptions on the datum but also extends the related framework from lebesgue spaces to refined weighted lorentz spaces

on the operator l f f log f abstract the present note deals with the operator l h 1 r n d r n which takes a given element f of the hardy space to the function f log f in general this function need not be locally integrable nevertheless due to peculiar cancellations of large positive and negative terms in the integral f log f with c 0 r n we are able to give meaning to f log f as a schwartz distribution we find several alternatives for this interpretation of f log f

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

besov spaces with variable smoothness and integrability abstract in this article we introduce besov spaces with variable smoothness and integrability indices we prove independence of the choice of basis functions as well as several other basic properties we also give sobolev type embeddings and show that our scale contains variable order holder zygmund spaces as special cases we provide an alternative characterization of the besov space using approximations by analytic functions

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

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 multiplicity of solutions for p x laplacian equations in rn abstract this paper investigates the existence and multiplicity of solutions for p x laplacian equations in r n

peak quasisymmetric functions and eulerian enumeration abstract via duality of hopf algebras there is a direct association between peak quasisymmetric functions and enumeration of chains in eulerian posets we study this association explicitly showing that the notion of cd index long studied in the context of convex polytopes and eulerian posets arises as the dual basis to a natural basis of peak quasisymmetric functions introduced by stembridge thus eulerian posets having a nonnegative cd index for example face lattices of convex polytopes correspond to peak quasisymmetric functions having a nonnegative representation in terms of this basis we diagonalize the operator that associates the basis of descent sets for all quasisymmetric functions to that of peak sets for the algebra of peak functions and study the g polynomial for eulerian posets as an algebra homomorphism

approximation by lupas beta integral operators abstract in the present article we introduce certain lupas beta operators which preserve constant as well as linear functions we define the operators in terms of hypergeometric series and establish moments using such approach asymptotic formula error estimation due to modulus of continuity and weighted approximation are studied we also establish the rate of convergence for those functions whose derivatives are of bounded variation

gradient estimates for higher order elliptic equations on nonsmooth domains abstract we establish optimal gradient estimates in orlicz space for a nonhomogeneous elliptic equation of higher order with discontinuous coefficients on a nonsmooth domain our assumption is that for each point and for each sufficiently small scale the coefficients have small mean oscillation and the boundary of the domain is sufficiently close to a hyperplane as a consequence we prove the classical w m p m 1 2 1 p estimates for such a higher order equation our results easily extend to higher order elliptic and parabolic systems

weighted orlicz estimates for general nonlinear parabolic equations over nonsmooth domains we introduce a parabolic analogue of muckenhoupt weights to study optimal weighted regularity in orlicz spaces for a general nonlinear parabolic problem of p laplacian type in divergence form over a nonsmooth domain assuming that the nonlinearity is measurable with respect to the time variable and has a small bounded mean oscillation bmo with respect to the spatial variables that the lateral boundary of the parabolic cylinder is reifenberg flat and that the associated weight belongs to a suitable parabolic muckenhoupt class we obtain a global gradient estimate for such a nonlinear parabolic problem by essentially proving that the gradient of the weak solution is as globally integrable as the nonhomogeneous term in the weighted orlicz space our results extend the existing regularity estimates in lebesgue spaces to weighted orlicz spaces

enriched p partitions and peak algebras abstract we develop a more general view of stembridge s enriched p partitions and use this theory to outline the structure of peak algebras for the symmetric group and the hyperoctahedral group initially we focus on commutative peak algebras spanned by sums of permutations with the same number of peaks where we consider several variations on the definition of peak whereas stembridge s enriched p partitions are related to quasisymmetric functions the dual coalgebra of solomon s type a descent algebra our generalized enriched p partitions are related to type b quasisymmetric functions the dual coalgebra of solomon s type b descent algebra using these functions we move on to explore non commutative peak algebras spanned by sums of permutations with the same set of peaks while some of these algebras have been studied before our approach gives explicit structure constants with a combinatorial description

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

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

eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent in this paper we are concerned with a new class of anisotropic quasilinear elliptic equations with a power like variable reaction term one of the main features of our work is that the differential operator involves partial derivatives with different variable exponents so that the functional analytic framework relies upon anisotropic sobolev and lebesgue spaces existence and nonexistence results are deeply influenced by the competition between the growth rates of the anisotropic coefficients our main results point out some striking phenomena related to the existence of a continuous spectrum in several distinct situations

szasz durrmeyer type operators based on charlier polynomials in the present paper we introduce a durrmeyer type modification of szasz operators based on charlier polynomials and study a voronovskaja type asymptotic theorem local approximation theorem weighted approximation statistical convergence and approximation of functions with derivatives of bounded variation for these operators

certain new classes of durrmeyer type operators in the present paper we estimate the rate of convergence for functions having bounded derivatives for certain durrmeyer type generalization of jain and pethe operators in the last section we also propose a new modification of the lupas operators and study some direct results we also give some open problems for the readers

harmonic type approximation lemmas we give a survey of known and not known harmonic type approximation lemmas which are descendants of the classical de giorgi s one and we outline some of their recent or possible applications

regularity of solutions to a class of variable exponent fully nonlinear elliptic equations abstract in the present paper we propose the investigation of variable exponent degenerate singular elliptic equations in non divergence form this current endeavor parallels the by now well established theory of functionals satisfying nonstandard growth condition which in particular encompasses problems ruled by the p x laplacian operator under rather general conditions we prove viscosity solutions to variable exponent fully nonlinear elliptic equations are locally of class c 1 for a universal constant 0 1 a key feature of our estimates is that they do not depend on the modulus of continuity of exponent coefficients and thus may be employed to investigate a variety of problems whose ellipticity degenerates and or blows up in a discontinuous fashion

higher integrability for minimizers of integral functionals with p q growth abstract we prove higher integrability for minimizers u r n of integral functionals f du a x u dx where f satisfies a non standard growth condition of p q type z p f z l 1 z q p

lp λ regularity for fully nonlinear elliptic equations abstract we establish the variable exponent morrey spaces l p estimate to the dirichlet problem for fully nonlinear elliptic equations on a c 1 1 bounded domain for variable exponents p and

integral operators on the halfspace in generalized lebesgue spaces lp part ii in this paper we generalize a version of the classical calderon zygmund theorem on principle value integrals in generalized lebesgue spaces lp proved in j reine angew math 563 2003 197 220 to kernels which do not satisfy standard estimates on rd 1 this result will be used in part ii of this paper to prove the classical theorem on halfspace estimates of agmon douglis and nirenberg comm pure appl math 12 1959 623 727 for generalized lebesgue spaces lp

higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients abstract in this paper based on the theory of variable exponent spaces we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients under suitable assumptions we obtain a local gradient estimate in orlicz space for weak solution

skew quasisymmetric schur functions and noncommutative schur functions abstract recently a new basis for the hopf algebra of quasisymmetric functions qsym called quasisymmetric schur functions has been introduced by haglund luoto mason van willigenburg in this paper we extend the definition of quasisymmetric schur functions to introduce skew quasisymmetric schur functions these functions include both classical skew schur functions and quasisymmetric schur functions as examples and give rise to a new poset l c that is analogous to young s lattice we also introduce a new basis for the hopf algebra of noncommutative symmetric functions nsym this basis of nsym is dual to the basis of quasisymmetric schur functions and its elements are the pre image of the schur functions under the forgetful map nsym sym we prove that the multiplicative structure constants of the noncommutative schur functions equivalently the coefficients of the skew quasisymmetric schur functions when expanded in the quasisymmetric schur basis are nonnegative integers satisfying a littlewood richardson rule analogue that reduces to the classical littlewood richardson rule under as an application we show that the morphism of algebras from the algebra of poirier reutenauer to sym factors through nsym we also extend the definition of schur functions in noncommuting variables of rosas sagan in the algebra ncsym to define quasisymmetric schur functions in the algebra ncqsym we prove these latter functions refine the former and their properties and project onto quasisymmetric schur functions under the forgetful map lastly we show that by suitably labeling l c skew quasisymmetric schur functions arise in the theory of pieri operators on posets

direct estimates for certain szasz type operators we deal with the modified forms of the szasz basis functions we introduce a new sequence of linear positive operators of durrmeyer type direct estimates for the new sequence have been discussed an open problem is also proposed the present paper deals with the modified forms of the szasz basis functions we propose a durrmeyer type operator having the basis functions in summation and integration due to jain 1972 and pa lta nea 2008 we establish some direct results which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation in the end we give an open problem for the readers

monotonicity of the cd index for polytopes we prove that the cd index of a convex polytope satisfies a strong monotonicity property with respect to the cd indices of any face and its link as a consequence we prove for d dimensional polytopes a conjecture of stanley that the cd index is minimized on the d dimensional simplex moreover we prove the upper bound theorem for the cd index namely that the cd index of any d dimensional polytope with n vertices is at most that of c n d the d dimensional cyclic polytope with n vertices

harnack s inequality and the strong p laplacian abstract we study solutions of the strong p laplace equation we show that in contrast to p laplace solutions these solutions satisfy the ordinary scale invariant harnack inequality as consequences we derive the strong maximum principle and global integrability of solutions

random walks on quasisymmetric functions abstract conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations spectral results are also obtained several important random walks are now realized this way stanley s qs distribution results from endomorphisms given by evaluation maps a shuffles result from the a th convolution power of the universal character and the tchebyshev operator of the second kind introduced recently by ehrenborg and readdy yields traditional riffle shuffles a conjecture of ehrenborg regarding the spectra for a family of random walks on ab words is proven a theorem of stembridge from the theory of enriched p partitions is also recovered as a special case

rate of convergence for certain families of summation integral type operators in this paper we study the rate of convergence for the iterative combinations of a certain family of linear positive operators in terms of higher order integral modulus of smoothness we have used the technique of linear approximating method namely steklov mean to prove the main result in the end we propose some other sequences of linear positive operators and obtain the recurrence formulae for the central moments voronovskaja type asymptotic formulae and error estimations

some results on modified szasz mirakjan operators abstract in this paper we study the mixed summation integral type operators having szasz and beta basis functions we extend the study of gupta and noor v gupta m a noor convergence of derivatives for certain mixed szasz beta operators j math anal appl 321 1 2006 1 9 and obtain some direct results in local approximation without and with iterative combinations in the last section are established direct global approximation theorems

abstract hardy spaces with variable exponents abstract in this paper we introduce the definition of abstract hardy spaces with variable exponents via the atomic decomposition and molecular decomposition we prove the continuity from our variable hardy space h a t o p into l p where p r n 0 1 0 p p 1 moreover we investigate the bilinear theory finally we give an application of the abstract hardy spaces with variable exponents

the peak algebra and the descent algebras of types b and d we show the existence of a unital subalgebra n of the symmetric group algebra linearly spanned by sums of permutations with a common peak set which we call the peak algebra we show that n is the image of the descent algebra of type b under the map to the descent algebra of type a which forgets the signs and also the image of the descent algebra of type d the algebra n contains a two sided ideal n which is defined in terms of interior peaks this object was introduced in previous work by nyman 2003 we find that it is the image of certain ideals of the descent algebras of types b and d we derive an exact sequence of the form 0 n n n 2 0 we obtain this and many other properties of the peak algebra and its peak ideal by first establishing analogous results for signed permutations and then forgetting the signs in particular we construct two new commutative semisimple subalgebras of the descent algebra of dimensions n and n 2 1 by grouping permutations according to their number of peaks or interior peaks we discuss the hopf algebraic structures that exist on the direct sums of the spaces n and n over n 0 and explain the connection with previous work of stembridge 1997 we also obtain new properties of his descents to peaks map and construct a type b analog

global gradient estimates for the parabolic p x t laplacian equation abstract in this paper we consider the global gradient estimates for weak solutions of the parabolic p x t laplacian type equation in a reifenberg flat domain

the singular set of minima of integral functionals in this paper we provide upper bounds for the hausdorff dimension of the singular set of minima of general variational integrals open image in new window where f is suitably convex with respect to dv and holder continuous with respect to x v in particular we prove that the hausdorff dimension of the singular set is always strictly less than n where open image in new window

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

global regularity for higher order divergence elliptic and parabolic equations abstract in this paper we obtain the global regularity estimates of the weak solutions in sobolev spaces and orlicz spaces for higher order elliptic and parabolic equations of divergence form with small bmo coefficients in the whole space we only focus on the parabolic case while the corresponding result in the elliptic case can be obtained as a corollary

on w1 p estimates for elliptic equations in divergence form first we will apply the method to study w 1 p regularity for a nonlinear elliptic operator in divergence form we would like to point out that in the particular case of a linear elliptic equation this method gives an alternative proof to the classical one which uses the general theory of singular integrals the utility of the method that we describe below is that hypotheses a and b are obtained directly by studying the deviation of the coefficients of a from the coefficients of a0 and this is usually not a difficult task a more interesting application of this kind of approximation method is to elliptic homogenization problems for which we obtain results that give w 1 p estimates with a weak hypothesis of regularity in the coefficients for instance we are able to study the following cases

lipschitz type smoothness of the fractional integral on variable exponent spaces fil ramseyer mauricio javier consejo nacional de investigaciones cientificas y tecnicas centro cientifico tecnologico conicet santa fe instituto de matematica aplicada del litoral universidad nacional del litoral instituto de matematica aplicada del litoral argentina

duality between quasi symmetrical functions and the solomon descent algebra abstract the ring qsym of quasi symmetric functions is naturally the dual of the solomon descent algebra the product and the two coproducts of the first extending those of the symmetric functions correspond to a coproduct and two products of the second which are defined by restriction from the symmetric group algebra a consequence is that qsym is a free commutative algebra

an eigenvalue problem with variable exponents abstract a highly nonlinear eigenvalue problem is studied in a sobolev space with variable exponent the euler lagrange equation for the minimization of a rayleigh quotient of two luxemburg norms is derived the asymptotic case with a variable infinity is treated local uniqueness is proved for the viscosity solutions

maximum principles for anisotropic elliptic inequalities we establish some maximum and comparison principles for weak distributional solutions of anisotropic elliptic inequalities in divergence form both in the homogeneous and non homogeneous case the main prototypes we have in mind are inequalities involving the p laplace operator and the generalized mean curvature operator

higher integrability for nonlinear elliptic equations with variable growth abstract in this paper based on the theory of variable exponent spaces we study the regularity for a class of nonlinear elliptic equation with p x laplacian under suitable assumptions we obtain a local gradient estimate in the orlicz space for weak solution

the peak algebra of the symmetric group revisited abstract the linear span p n of the sums of all permutations in the symmetric group sn with a given set of peaks is a sub algebra of the symmetric group algebra due to nyman this peak algebra is a left ideal of the descent algebra d n and the direct sum p of all p n is a hopf sub algebra of the direct sum d of all d n dual to the stembridge algebra of peak functions in our self contained approach peak counterparts of several results on the descent algebra are established including a simple combinatorial characterization of the algebra p n an algebraic characterization of p n based on the action on the poincare birkhoff witt basis of the free associative algebra the display of peak variants of the classical lie idempotents an eulerian type sub algebra of p n a description of the jacobson radical of p n and its nil potency index of the principal indecomposable and irreducible p n modules and of the cartan matrix of p n furthermore it is shown that the primitive lie algebra of p is free and that p is its enveloping algebra

mappings of bmo bounded distortion this paper can be viewed as a sequel to the work 9 where the theory of mappings of bmo bounded distortion is developed largely in even dimensions using singular integral operators and recent developments in the theory of higher integrability of jacobians in hardy orlicz spaces in this paper we continue this theme refining and extending some of our earlier work as well as obtaining results in new directions the planar case was studied earlier by g david 4 in particular he obtained existence theorems modulus of continuity estimates and bounds on area distortion for mappings of bmo distortion in fact in slightly more generality we obtain similar results in all even dimensions one of our main new results here is the extension of the classical theorem of painleve concerning removable singularties for bounded analytic functions to the class of mappings of bmo bounded distortion the setting of the plane is of particular interest and somewhat more can be said here because of the existence theorem or the measurable riemann mapping theorem which is not available in higher dimensions we give a construction to show our results are qualitatively optimal another surprising fact is that there are domains which support no bounded quasiregular mappings but admit

elliptic equations with bmo coefficients in lipschitz domains in this paper we study inhomogeneous dirichlet problems for elliptic equations in divergence form optimal regularity requirements on the coefficients and domains for the w 1 p 1 p estimates are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo semi norms the domain is supposed to have lipschitz boundary with small lipschitz constant these conditions for the w 1 p theory do not just weaken the requirements on the coefficients they also lead to a more general geometric condition on the domain

moment estimations of new szasz mirakyan durrmeyer operators jain 1972 introduced the modified form of the szasz mirakjan operator based on certain parameter 0 1 several modifications of the operators proposed and are available in the literature here we consider actual durrmeyer variants of the operators due to jain it is observed here that the durrmeyer variant have nice properties and one need not to take any restriction on in order to obtain convergence we establish moments using the tricomi s confluent hypergeometric function and stirling numbers of first kind and also estimate some direct results

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

local calderon zygmund estimates for parabolic minimizers abstract we establish local calderon zygmund estimates for parabolic minimizers u to certain variational inequalities the formal corresponding parabolic partial differential equation would be t u div f z u d u u f z u d u div f p 2 f h with p 2 n n 2 however since we do not impose any condition on the existence of the derivative u f the pde above may not have any meaning at all for proving the calderon zygmund estimates we thus remain solely on the level of parabolic minimizers precisely for q p we prove that d u l loc q if u is locally holder continuous and f l loc q and h l loc q for a q depending on q

riesz potential estimates for a class of double phase problems abstract a double phase problem with a bounded borel measure on the right hand side is studied we prove an optimal pointwise gradient estimate for such a measure data problem via riesz potentials of the measure under log dini continuity assumption on the modulating coefficients as a consequence we find an optimized c 1 regularity criterion

peak algebras paths in the bruhat graph and kazhdan lusztig polynomials we obtain a nonrecursive combinatorial formula for the kazhdan lusztig polynomials which holds in complete generality and which is simpler and more explicit than any existing one and which cannot be linearly simplified our proof uses a new basis of the peak subalgebra of the algebra of quasisymmetric functions

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

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

on the distribution of surface extrema in several one and two dimensional random landscapes we study here a standard next nearest neighbor nnn model of ballistic growth on one and two dimensional substrates focusing our analysis on the probability distribution function p m l of the number m of maximal points i e local peaks of growing surfaces our analysis is based on two central results i the proof presented here of the fact that uniform one dimensional ballistic growth process in the steady state can be mapped onto rise and descent sequences in the ensemble of random permutation matrices and ii the fact established in ref g oshanin and r voituriez j phys a math gen 37 6221 2004 that different characteristics of rise and descent patterns in random permutations can be interpreted in terms of a certain continuous space hammersley type process for one dimensional system we compute p m l exactly and also present explicit results for the correlation function characterizing the enveloping surface for surfaces grown on 2d substrates we pursue similar approach considering the ensemble of permutation matrices with long ranged correlations determining exactly the first three cumulants of the corresponding distribution function we define it in the scaling limit using an expansion in the edgeworth series and show that it converges to a gaussian function as l