On the Boundary Point Principle for divergence-type equations

TL;DR

This paper extends the boundary point principle to divergence-type elliptic and parabolic equations, establishing versions of the Zaremba-Hopf-Oleinik lemma under optimal conditions on coefficients and domain boundaries.

Contribution

It introduces new versions of the boundary point lemma for divergence-form equations with sharp conditions on coefficients and boundary regularity.

Findings

Established boundary point lemmas for divergence equations

Provided sharp conditions on coefficients and boundary regularity

Extended classical results to more general divergence-type equations

Abstract

We provide some versions of the Zaremba-Hopf-Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coefficients of equations and on the boundaries of domains.