W0 1,1 Solutions of Elliptic Equations with Degenerate Coercivity

Abstract

The Sobolev space W0 1,2(Ω) is the natural functional framework to find weak solutions of nonlinear elliptic problems of the following type (P)    −div³ a(x)∇u (1+|u|) θ ´ = f (x) in Ω, u = 0 on ∂Ω. where the function f belongs to the dual space of L m(Ω) with m > 1, Ω is a bounded open subset of R N , with N > 2, θ is a real number such that 0 ≤ θ ≤ 1, and a : Ω → R is a α ≤ a(x) ≤ β, for almost every x ∈ Ω, where α and β are positive constants.