Existence of renormalized solutions to nonlinear elliptic equations with lower-order terms and right-hand side measure

Abstract

In this paper we prove the existence of a solution for a class of non coercive nonlinear equations whose prototype is: −Δ pu+b(x)|∇u| λ=μ in Ω, u=0 on ∂Ω, where Ω is a bounded open subset of R N , N⩾2, Δ p is the so called p-Laplace operator, 1< p< N, μ is a Radon measure with bounded variation on Ω, 0⩽ λ⩽ p−1 and b belongs to the Lorentz space L N,1(Ω) .