Boundary weak Harnack estimates and quantitative strong maximum principles for uniformly elliptic PDE

TL;DR

This paper extends key boundary estimates, specifically the weak Harnack inequality and the quantitative strong maximum principle, to uniformly elliptic PDEs in non-divergence form, enhancing understanding of boundary behavior.

Contribution

It provides full boundary extensions of two fundamental estimates for uniformly elliptic PDEs in non-divergence form, which was previously unestablished.

Findings

Boundary weak Harnack estimates established

Quantitative strong maximum principle extended to boundary cases

Enhanced boundary regularity results for elliptic PDEs

Abstract

We give full boundary extensions to two fundamental estimates in the theory of elliptic PDE, the weak Harnack inequality and the quantitative strong maximum principle, for uniformly elliptic equations in non-divergence form.