Some remarks on uniform boundary Harnack Principles

TL;DR

This paper establishes two domain-independent boundary Harnack principles, enhancing understanding of harmonic functions near boundaries without domain-specific constants.

Contribution

It introduces two versions of boundary Harnack principles with constants independent of the domain, advancing theoretical knowledge in potential theory.

Findings

Proved domain-independent boundary Harnack principles

Extended boundary Harnack principles to new settings

Improved understanding of harmonic functions near boundaries

Abstract

We prove two versions of a boundary Harnack principle in which the constants do not depend on the domain.