Weighted a priori estimates for the Poisson equation

Abstract

Abstract. Let Ω be a bounded domain in Rn with ∂Ω ∈ C2 and let u be a solution of the classical Poisson problem in Ω; i.e., −∆u = f in Ω u = 0 on ∂Ω where f ∈ Lpω(Ω) and ω is a weight in Ap. The main goal of this paper is to prove the following a priori estimate