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

Abstract

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 R N , N 2 and(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. AMS Subject Classifications: 35J20, 35J25, 35J60Chinese Library Classifications: O175.29