Boundary weak Harnack estimates and regularity for elliptic PDE in divergence form

We obtain a global extension of the classical weak Harnack inequality which ex-tends and quantifies the Hopf-Oleinik boundary-point lemma, for uniformly elliptic equations in divergence form. Among the consequences is a boundary gradient estimate, due to Krylov and well-studied for non-divergence form equations, but completely novel in the divergence framework. Another consequence is a new more general version of the Hopf-Oleinik lemma. & COPY; 2023 Published by Elsevier Ltd.

Automated summary

In this paper, a global extension of the classical weak Harnack inequality is obtained, which extends and quantifies the Hopf-Oleinik boundary-point lemma for uniformly elliptic equations in divergence form. Among the consequences are a boundary gradient estimate, proposed by Krylov and well studied for non-divergence form equations, but completely novel in the divergence framework, and a new more general version of the Hopf-Oleinik lemma.