Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space

Abstract

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion b(u)−div(a(x,Du)+F(u))∋ f in W where f ∈ L 1 (W). A vector field a(.,.) is a Caratheodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general L 1 -data. AMS subject classifications: 35J15, 35J70, 35J85