Existence and nonexistence of a solution for a nonlinear \(p(x)\)-elliptic problem with right-hand side measure
type: Item
instance of: scholarly article
title: Existence and nonexistence of a solution for a nonlinear \(p(x)\)-elliptic problem with right-hand side measure
zbMATH Open document ID: 1390.35389
DOI: 10.1155/2014/320527
author: E. Azroul
author: Abdelkrim Barbara
author: Hicham Redwane
published in: International Journal of Analysis
publication date: 2018-06-11T00:00:00Z
review text: Summary: We discuss the existence and nonexistence of solution of a nonlinear problem \(p(x)\)-elliptic-\(\operatorname{div}(a(x, \nabla u))+g(x, u, \nabla u)=\mu\), where \(\mu\) is a Radon measure with bounded total variation, by considering the Sobolev spaces with variable exponents. This study is done in two cases: (i) \(\mu\) is absolutely continuous with respect to \(p(x)\)-capacity and (ii) \(\mu\) is concentrated on a Borel set of null \(p(x)\)-capacity.
Mathematics Subject Classification ID: 35R06
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A35
zbMATH DE Number: 6883045
zbMATH Keywords: existence of solution
zbMATH Keywords: PDE with Radon measure
zbMATH Keywords: \(p(x)\)-elliptic problem
zbMATH Keywords: Sobolev spaces with variable exponents
Wikidata QID: Q59041347
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/320527
OpenAlex ID: W2083333079
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description: scientific article; zbMATH DE number 6883045