the neumann problem for the laplacian and the monge kantorovich mass transfer problem abstract we consider the natural neumann boundary condition for the laplacian we study the limit as p of solutions of p u p 0 in a domain with d u p p 2 u p g on we obtain a natural minimization problem that is verified by a limit point of u p and a limit problem that is satisfied in the viscosity sense it turns out that the limit variational problem is related to the monge kantorovich mass transfer problems when the measures are supported on

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

convergence relation between p x harmonic maps and minimizers of p x energy functional with penalization abstract we prove that the p x ginzburg landau type minimizers converge to the p x harmonic maps the location of zeros of the minimizers is presented in the case of p x 1 2 when p x 2 there exists no zero of the minimizers in the domain in addition the convergence rate of the modulus of the minimizers to 1 is estimated

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

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

a tour of the theory of absolutely minimizing functions a detailed analysis of the class of absolutely minimizing functions in euclidean spaces and the relationship to the infinity laplace equation

the behaviour of the p x laplacian eigenvalue problem as p x abstract in this paper we study the behaviour of the solutions to the eigenvalue problem corresponding to the p x laplacian operator div u p x 2 u p x u p x 2 u in u 0 on as p x we consider a sequence of functions p n x that goes to infinity uniformly in under adequate hypotheses on the sequence p n namely that the limits ln p n x x and p n n x q x exist we prove that the corresponding eigenvalues p n and eigenfunctions u p n verify that p n 1 n u p n u uniformly in where u is a nontrivial viscosity solution of the following problem min u u 2 log u u u q u q 0 in u 0 on

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

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

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

galois descent of semi affinoid spaces we study the galois descent of semi affinoid non archimedean analytic spaces these are the non archimedean analytic spaces which admit an affine special formal scheme as model over a complete discrete valuation ring such as for example open or closed polydiscs or polyannuli using weil restrictions and galois fixed loci for semi affinoid spaces and their formal models we describe a formal model of a k analytic space x provided that x otimes kl is semi affinoid for some finite tamely ramified extension l of k as an application we study the forms of analytic annuli that are trivialized by a wide class of galois extensions that includes totally tamely ramified extensions in order to do so we first establish a weierstrass preparation result for analytic functions on annuli and use it to linearize finite order automorphisms of annuli finally we explain how from these results one can deduce a non archimedean analytic proof of the existence of resolutions of singularities of surfaces in characteristic zero

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

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

existence of solutions for systems arising in electromagnetism abstract in this paper we study the following p x curl systems u p x 2 u a x u p x 2 u f x u g x u u 0 in u p x 2 u n 0 u n 0 on where r 3 is a bounded simply connected domain with a c 1 1 boundary denoted by p 1 is a continuous function a l f g r 3 r 3 are caratheodory functions and are two parameters using variational arguments based on fountain theorem and dual fountain theorem we establish some existence and non existence results for solutions of this problem our main results generalize the results of xiang et al 2017 41 bahrouni and repovs 2018 9 and ge and lu 2019 22

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

invariance theorems concerning reflection at numerical boundaries abstract downwind computational boundaries in the numerical approximation of hyperbolic equations are in general not transparent and they create spurious reflection a useful measure of this is given by the energy or usual sum of squares of the reflected solution in response to an arbitrary solution which originates from within the computing domain we prove in that respect a somewhat unexpected property namely that for those full discretizations which are obtained by applying to a space discretization of the equations an energy conservative discrete time marching method the energy reflected at the boundary is independent of the value of t and is strictly equal to the energy reflected in the semidiscrete case this is verified in numerical experiments optimal boundary equations may be defined in the semidiscrete case of those which maximize the rate of convergence to zero of the reflected energy when h 0 a corollary of the preceding result is that those boundary equations remain optimal in the same sense when used in an energy conservative full discretization moreover this convergence result continues to hold when a nonconservative but stable i e dissipative time discretization is used this is verified numerically with the first order adams predictor corrector method the results of this paper are derived with the mathematics of the simple three point central difference discretization of spatial derivatives obvious generalizations to other cases are mentioned at the end of the paper

on a weighted inequality of hardy type in spaces lp abstract the boundedness of hardy type operator h f x t r n t x f t d t is studied in weighted variable exponent lebesgue spaces l p the necessary and sufficient criterion established on the weight functions v x x and exponents p x q x for the hardy operator to be bounded from l p to l q v the exponents satisfy a modified logarithmic condition near zero and at infinity 0 f f 0 r sup x b 0 f x f 0 ln 1 w x n 1 sup x r n b 0 n f x f ln w x where w x t r n t x 1 p t 1 t d t

phragmen lindelof theorems for equations with nonstandard growth abstract the phragmen lindelof theorem on unbounded domains is studied for subsolutions of variable exponent p laplace equations of homogeneous and nonhomogeneous types the discussion is illustrated by a number of examples of unbounded domains such as half space angular domains and domains narrowing at infinity our approach gives some new results also in the setting of the p laplacian and the harmonic operator

on the axiomatic approach to harnackʼs inequality in doubling quasi metric spaces abstract we introduce a novel approach towards harnack s inequality in the context of spaces of homogeneous type this approach based on the so called critical density property and doubling properties for weights avoids the explicit use of covering lemmas and bmo

development of a non reflecting boundary condition for multidimensional nonlinear duct acoustic computation the quality of any time domain nonlinear cfd simulation of silencers is determined by the modeling procedure used for the anechoic termination at the boundary end of the computational domain in this study a novel anechoic boundary condition based on the characteristic theory combined with the linear relaxation method has been developed in an open source cfd code wave propagation in ducts and mufflers has been analyzed and the effect of the damping properties of the boundary condition has been studied the study shows that the explicit damping of the solution vector produces good performance at all the frequencies with acoustic waves having varying incidence to the boundary also results indicate that numerical reflection of acoustic waves with high incident angles is reduced if the damping is applied at the boundary within the semi implicit solution of the governing equations finally the boundary condition has been applied together with a nonlinear solver to evaluate the acoustic attenuation performance of circular flow reversing chambers and single plug perforated mufflers with and without mean flow velocity of the gas code validation has been carried out against experimental data

limits as p x of p x harmonic functions abstract in this note we study the limit as p x of solutions to p x u 0 in a domain with dirichlet boundary conditions our approach consists in considering sequences of variable exponents converging uniformly to and analyzing how the corresponding solutions of the problem converge and which equation is satisfied by the limit

regularity for the porous medium equation with variable exponent the singular case abstract we extend to the singular case the results of e henriques j m urbano intrinsic scaling for pdes with an exponential nonlinearity indiana univ math j 55 5 2006 1701 1721 concerning the regularity of weak solutions of the porous medium equation with variable exponent the method of intrinsic scaling is used to show that local weak solutions are locally continuous

variable exponent functionals in image restoration abstract we study a functional with variable exponent 1 p x 2 which provides a model for image denoising and restoration here p x is defined by the gradient information in the observed image the diffusion derived from the proposed model is between total variation based regularization and gaussian smoothing the diffusion speed of the corresponding heat equation is tuned by the variable exponent p x the minimization problem and its associated flow in a weakened formulation are discussed the existence uniqueness stability and long time behavior of the proposed model are established in the variable exponent functional space w 1 p x experimental results illustrate the effectiveness of the model in image restoration

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

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

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

embeddings of variable hajlasz sobolev spaces into holder spaces of variable order pointwise estimates in variable exponent sobolev spaces on quasi metric measure spaces are investigated based on such estimates sobolev embeddings into holder spaces with variable order are obtained this extends some known results to the variable exponent setting

renormalized solutions for a nonlinear parabolic equation with variable exponents and l 1 data abstract we prove the well posedness existence and uniqueness of a renormalized solution to nonlinear parabolic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev spaces with variable exponents

influence of momentum interpolation methods on the accuracy and convergence of pressure velocity coupling algorithms in openfoam checkerboard pressure is one of the most significant problems arising from the use of collocated grids for fluid dynamic simulations using the finite volume method the original rhie chow momentum interpolation technique termed original momentum interpolation method omim was proposed to eliminate the non physical saw tooth pressure oscillations however it was soon proved that the steady state solutions obtained with this technique were under relaxation factor dependent nevertheless standard omim is still commonly used in several cfd codes like openfoam the software used for this work in this paper the omim and a possible correction for under relaxation dependency which has been implemented in openfoam are discussed in detail the proposed methodology is compared and contrasted with omim in terms of accuracy of the solution and speed of convergence for several classical pressure velocity segregated algorithms for steady state solvers namely simple simple c simple r and piso a classical laminar 2d cavity is used as the base test case the study is then extended to a more complex 2d airfoil profile naca0012 in the cases considered mesh uniformity and orthogonality are progressively reduced and turbulence starts playing an important role limiting therefore the convergence of the cases and the performance of the correction

function spaces of variable smoothness and integrability abstract in this article we introduce triebel lizorkin spaces with variable smoothness and integrability our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years vector valued maximal inequalities do not work in the generality which we pursue and an alternate approach is thus developed using it we derive molecular and atomic decomposition results and show that our space is well defined i e independent of the choice of basis functions as in the classical case a unified scale of spaces permits clearer results in cases where smoothness and integrability interact such as sobolev embedding and trace theorems as an application of our decomposition we prove optimal trace theorem in the variable indices case

a homogenization process for the strong p x laplacian abstract in this work we analyze a homogenization process that takes place in a problem involving the strong p x laplacian precisely we consider the following problem closely related with tug of war games a x e u x b x e u x 0 x u x g x x with a b continuous functions such that a b 1 and b 0 for every x being e the homogenization parameter classical results in regularity theory yield the convergence of at least a subsequence of u e to some continuous function as e 0 we determine the equation verified by this limit as well as some of its properties

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

toute forme moderement ramifiee d un polydisque ouvert est triviale let k be a complete non archimedean field and let x be a k analytic space assume that there exists a finite tamely ramified extension l of k such that x l is isomorphic to an open polydisc over l we prove that x is itself isomorphic to an open polydisc over k the proof consists in using the graded reduction a notion which is due to temkin of the algebra of functions on x together with some graded counterparts of classical commutative algebra results nakayama s lemma going up theorem basic notions about etale algebras etc

holder regularity for the gradients of solutions of the strong p x laplacian abstract under some assumptions on the continuous function p x 1 we obtain the local c 1 regularity of solutions of the strong p x laplacian div u p x 2 u u p x 2 log u u p 0 by using the integral estimates in campanato spaces

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

finite element and boundary element modelling for the acoustic wave transmission in mean flow medium the frequency characteristics of the acoustic wave transmission in a medium with mean flow are considered one approach is to solve the helmholtz equation with mean flow medium in original co ordinates which is directly discretized for the one dimensional and the axisymmetric fem another approach is to transform the equation into the standard helmholtz equation which is discretized for the axisymmetric fem and the three dimensional bem the numerical models are examined first for a straight circular duct the solutions by the numerical approaches are compared with the analytical solution the examination is then extended to the case when the mean flow is locally present in the muffler with expansion chamber to model the spatial mean flow in the bem model the partitioned domain approach is also developed no shear effect between the two regions are included