On the Boundary Harnack Principle for operators with different lower order terms

TL;DR

This paper establishes the Boundary Harnack principle for solutions to two different elliptic equations with the same principal part in Lipschitz domains, extending classical results to more general operators.

Contribution

It proves the Boundary Harnack principle for two different elliptic operators with the same principal part in Lipschitz domains, a novel extension of classical theory.

Findings

Boundary Harnack principle holds for solutions to different elliptic operators

Results apply to Lipschitz domains with Lipschitz boundaries

Extends classical boundary behavior results to more general operators

Abstract

We provide the classical Boundary Harnack principle in Lipschitz domains for solutions to two different linear uniformly elliptic equations with the same principal part.