Existence and Regularity of Solution for Strongly Nonlinear p(x)-Elliptic Equation with Measure Data (Journal of Partial Differential Equations, 2018)
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