Existence of solutions for some nonlinear elliptic unilateral problems with measure data

Abstract

In this paper we prove the existence of entropy solution to unilateral problems associated to the equations of the type: $Au-div(\phi(u))=\mu\in L^{1}(\Omega)+W^{-1,p'(x)}(\Omega)$, where $A$ is a Leray-Lions operator acted from $W_{0}^{1,p(x)}(\Omega)$ into its dual $W^{-1,p(x)}(\Omega)$ and $\phi\in C^{0}(R,R^{N})$.