Weighted a priori estimates for solution of (-Δ)mu = f with homogeneous dirichlet conditions

Abstract

Let u be a weak solution of (-Δ)mu = f with Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ Rn. Then, the main goal of this paper is to prove the following a priori estimate: {double pipe}u{double pipe}Wω 2m,p(Ω) ≤ C{double pipe}f{double pipe}Lω p(Ω), where ω is a weight in the Muckenhoupt class