Volume 30, Issue 1
Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data

J. Part. Diff. Eq., 30 (2017), pp. 31-46.

Published online: 2017-03

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• 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.

• Keywords

Sobolev spaces with variable exponents strongly nonlinear p(x)-elliptic equations with measure data regularity

35J20, 35J25, 35J60

cherif_hassib@yahoo.fr (Moulay Cherif Hassib)

akdimyoussef@yahoo.fr (Youssef Akdim)

azroulelhoussine@gmail.com (Elhoussine Azroul)

abdelkrimbarbara@gmail.com (Abdelkrim Barbara)

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• RIS
• TXT
@Article{JPDE-30-31, author = {Hassib , Moulay Cherif and Akdim , Youssef and Azroul , Elhoussine and Barbara , Abdelkrim }, title = {Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data}, journal = {Journal of Partial Differential Equations}, year = {2017}, volume = {30}, number = {1}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v30.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/5069.html} }
TY - JOUR T1 - Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data AU - Hassib , Moulay Cherif AU - Akdim , Youssef AU - Azroul , Elhoussine AU - Barbara , Abdelkrim JO - Journal of Partial Differential Equations VL - 1 SP - 31 EP - 46 PY - 2017 DA - 2017/03 SN - 30 DO - http://doi.org/10.4208/jpde.v30.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/5069.html KW - Sobolev spaces with variable exponents KW - strongly nonlinear p(x)-elliptic equations with measure data KW - regularity AB - 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.
Moulay Cherif Hassib, Youssef Akdim, Elhoussine Azroul & Abdelkrim Barbara. (2019). Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data. Journal of Partial Differential Equations. 30 (1). 31-46. doi:10.4208/jpde.v30.n1.3
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