Existence and uniqueness of entropy solutions for some nonlinear elliptic unilateral problems in Musielak-Orlicz-Sobolev spaces

Abstract

In this paper, we study the existence and uniqueness of entropy solutions for some quasilinear degenerate elliptic unilateral problems of the type

- div a(x,\nabla u) = f     in    \Omega,
u= 0                             on     \partial\Omega,

in the Musielak-Orlicz-Sobolev spaces   W_{0}^{1} L_{\varphi}(\Omega), with  f \in L^{1}(\Omega).