On the Parabolic Boundary Harnack Principle

TL;DR

This paper extends the parabolic Boundary Harnack Principle to less regular space-time domains, including slit domains, using analytical methods adapted from elliptic cases, for both divergence and non-divergence operators.

Contribution

It introduces new analytical techniques to establish the Boundary Harnack Principle in complex, irregular space-time domains for parabolic operators.

Findings

Established Boundary Harnack Principle in slit domains.

Extended results to both divergence and non-divergence operators.

Developed methods from elliptic to parabolic context.

Abstract

We investigate the parabolic Boundary Harnack Principle for both divergence and non-divergence type operators by the analytical methods we developed in the elliptic context. Besides the classical case, we deal with less regular space-time domains, including slit domains.