Marcela Sanmartino y Marisa Toschi

Weighted a priori estimates for the solution of the homogeneous Dirichlet problem for the powers of the Laplacian Operator

Let $u$ be a weak solution of $ (-Δ)^m u=f $ with Dirichlet boundary conditions in a smooth bounded domain $Ω\subset \mathbb{R}^n$. Then, the main goal of this paper is to prove the following a priori estimate: $$ \|u\|_{W^{2m,p}_ω(Ω)} \le C\, \|f\|_{L^p_ω(Ω)}, $$ where $ω$ is a weight in the Muckenhoupt class $A_p.$