Existence of a renormalized solution for some nonlinear anisotropic elliptic problems

Abstract

In this paper, we study a general class of nonlinear anisotrpic elliptic problems associated with the differential inclusion β(u) - div(a(x, D(u) + F(u)) ∋ f in Ω, where f ∈ L^∞(Ω). A vector field a(. , .) is a Caratheodory function. Using trunction techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for L^∞-data.