TY - JOUR
T1 - Existence and Regularity of Solution for Strongly Nonlinear <em>p(x)</em>-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 $\mathbb{R}$<sup>N</sup>, N ≥ 2 and A(u)=-div(a(x,u,∇u)) is a Leray-Lions operator defined from W<sup>1,p(x)</sup><sub>0</sub> (Ω) in to its dual W<sup>-1,p&#39;(x)</sup>(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.