Existence and uniqueness of renormalized solution to multivalued homogeneous Neumann problem with L1-data

Abstract

 In this paper, we discuss the existence and uniqueness of renormalized solution to nonlinear multivalued elliptic problem  β(u)-div a(x, Du) ∈ f with homogeneous Neumann boundary conditions and L¹ -data. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. Some a-priori estimates are used to obtain our results.