Existence of entropy solutions for some nonlinear problems in Orlicz spaces (Q1608791)

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