p-Laplacian type equations involving measures

Abstract

This is a survey on problems involving equations $-\operatorname{div}{\Cal A}(x,\nabla u)=μ$, where $μ$ is a Radon measure and ${\Cal A}:\bold {R}^n\times\bold R^n\to \bold R^n$ verifies Leray-Lions type conditions. We shall discuss a potential theoretic approach when the measure is nonnegative. Existence and uniqueness, and different concepts of solutions are discussed for general signed measures.