Existence and Regularity of Solution for Strongly Nonlinear <em>p(x)</em>-Elliptic Equation with Measure Data

Existence and Regularity of Solution for Strongly Nonlinear <em>p(x)</em>-Elliptic Equation with Measure Data

Year:    2017

Author:    Moulay Cherif Hassib, Youssef Akdim, Elhoussine Azroul, Abdelkrim Barbara

Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 1 : pp. 31–46

Abstract

The first part of this paper is devoted to study the existence of solution for nonlinear p(x) elliptic problem A(u)=μ in Ω, u =0 on ∂Ω, with a right-hand side measure, where Ω is a bounded open set of $\mathbb{R}$N, N ≥ 2 and A(u)=-div(a(x,u,∇u)) is a Leray-Lions operator defined from W1,p(x)0 (Ω) in to its dual W-1,p'(x)(Ω). However the second part concerns the existence solution, of the following setting nonlinear elliptic problems A(u)+g(x,u,∇u)=μ in Ω, u=0 on ∂Ω. We will give some regularity results for these solutions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v30.n1.3

Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 1 : pp. 31–46

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Sobolev spaces with variable exponents

Author Details

Moulay Cherif Hassib

Youssef Akdim

Elhoussine Azroul

Abdelkrim Barbara

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