Existence of entropy solutions for some nonlinear problems in Orlicz spaces

Abstract

We study in the framework of Orlicz Sobolev spaces $W_0^1{L}_M\left(\Omega \right)$, the existence of entropic solutions to the nonlinear elliptic problems: $-\text{div}a\left(\text{x,u,}\nabla u\right)+\text{div}\Phi \left(u\right)=f\text{in}\Omega$, for the case where the second member of the equation $f\in L^1\left(\Omega \right)$, and $\Phi \in {\left(C^0\left(ℝ\right)\right)}^N$.