Global $W^{2,p}$ estimates for elliptic equations in the non-divergence form

TL;DR

This paper proves global $W^{2,p}$ regularity estimates for solutions to uniformly elliptic equations in non-divergence form within Lipschitz polyhedral domains, advancing understanding of elliptic PDEs in nonsmooth geometries.

Contribution

It establishes the first global $W^{2,p}$ estimates for elliptic equations in non-divergence form on Lipschitz polyhedral domains.

Findings

Proves global $W^{2,p}$ estimates for elliptic equations in Lipschitz polyhedra.

Extends regularity theory to nonsmooth domain geometries.

Provides tools for further analysis of elliptic PDEs in complex domains.

Abstract

This paper is devoted to establishing global $W^{2, p}$ estimate for strong solutions to the Dirichlet problem of uniformly elliptic equations in the non-divergence form where the domain is a Lipschitz polyhedra.