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Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data
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@Article{JPDE-30-31,
author = {Hassib , Moulay CherifAkdim , YoussefAzroul , 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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