Weighted a Priori Estimates for the Poisson Equation

Abstract

Let Ω be a bounded domain in R n with C 2 and let u be a solution of the classical Poisson problem in ; i.e., { u = f in , u = 0 on , where f L p ( ) and is a weight in A p . The main goal of this paper is to prove the following a priori estimate u W 2 , p ( ) C f L p ( ), and to give some applications for weights given by powers of the distance to the boundary.