Nonlinear Neumann problems on bounded Lipschitz domains

Abstract

We prove existence and uniqueness, up to a constant, of an entropy solution to the nonlinear and non homogeneous Neumann problem -div [a(., ∇u)] + β(u) = ƒ in Ω ∂u / ∂va + γ(τu) = g on ∂Ω. Our approach is based essentially on the theory of m-accretive operators in Banach spaces, and in order preserving properties.