Generalizing Hopf's boundary point lemma

TL;DR

This paper extends Hopf's boundary point lemma to weak solutions of linear divergence form elliptic equations with Hölder continuous coefficients and Morrey space lower-order coefficients.

Contribution

It provides a new boundary point lemma applicable to elliptic equations with less regular coefficients, broadening the classical results.

Findings

Established Hopf's lemma for weak solutions with Hölder continuous coefficients.

Extended boundary point principles to equations with Morrey space lower-order coefficients.

Applicable to a wider class of elliptic PDEs with minimal regularity assumptions.

Abstract

We give a Hopf boundary point lemma for weak solutions of linear divergence form uniformly elliptic equations, with H$\ddot{\text{o}}$lder continuous top-order coefficients and lower-order coefficients in a Morrey space.