An approximation of Hedberg's type in Sobolev spaces with variable exponent and application
type: Item
instance of: scholarly article
title: An approximation of Hedberg's type in Sobolev spaces with variable exponent and application
zbMATH Open document ID: 1307.35101
DOI: 10.1155/2014/549051
author: A. Benkirane
author: Mostafa El Moumni
author: Aziz Fri
published in: Chinese Journal of Mathematics
publication date: 2014-10-16T00:00:00Z
review text: Summary: The aim of this paper is to extend the usual framework of PDE with \(A(u)=-\operatorname{div}a(x,u,\nabla u)\) to include a large class of cases with \(A(u)=\sum_{|\beta|\leq\alpha}(-1)^{|\beta|}D^\beta A_\beta (x,u,\nabla u,\dots ,\nabla^\alpha u)\), whose coefficient \(A_\beta\) satisfies conditions (including growth conditions) which guarantee the solvability of the problem \(A(u)=f\). This new framework is conceptually more involved than the classical one includes many more fundamental examples. Thus our main result can be applied to various types of PDEs such as reaction-diffusion equations, Burgers type equation, Navier-Stokes equation, and \(p\)-Laplace equation.
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6356652
Wikidata QID: Q59036453
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/549051
OpenAlex ID: W2167945022
cites work: Q5682705
cites work: A strongly nonlinear elliptic boundary value problem
cites work: Boundary Value Problems for Strongly Nonlinear Elliptic Equations
cites work: Two approximation problems in function spaces
cites work: A property of sobolev spaces
cites work: A generalization of a theorem of H.Brezis \& F.E.Browder and applications to some unilateral problems
cites work: Approximations de type Hedberg dans les espaces $W^m L \log L\left( \Omega \right)$ et applications
cites work: An approximation theorem in higher order Orlicz-Sobolev spaces and applications
cites work: Q4879410
cites work: Bessel potential spaces with variable exponent
cites work: Q4820901
cites work: Q4458796
cites work: Maximal function on generalized Lebesgue spaces L^p(⋅)
cites work: Hardy-Littlewood maximal operator on L^p(x) (ℝ)
cites work: Q4858060
cites work: Q5607484
cites work: On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
description: scientific article; zbMATH DE number 6356652