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

2010/06/07 by Ricardo G. Durán, Ricardo Duran, Duran, Ricardo +2
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1006.1337

arxiv created 2010/06/07 · openalex publication_date 2010/06/07 · arxiv updated 2010/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let u be a weak solution of (-Δ)^m u=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: ‖u‖_W^2m,pω(Ω) ≤ C ‖f‖_L^pω(Ω), where ω is a weight in the Muckenhoupt class A_p.

Related

• Weighted a priori estimates for elliptic equations
• Weighted-W^1,p estimates for weak solutions of degenerate and singular elliptic equations
• A priori estimates for some elliptic equations involving the p-Laplacian
• Weighted Calderón-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations
• The Dirichlet problem for the uniformly higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces