Parabolic Lipschitz truncation for multi-phase problems: the degenerate case

TL;DR

This paper develops a Lipschitz truncation technique tailored for parabolic multi-phase problems, utilizing Whitney decomposition and covering lemmas to handle phase distinctions.

Contribution

It introduces a novel Lipschitz truncation method specifically designed for degenerate multi-phase parabolic problems, enhancing phase distinction and analysis.

Findings

Effective Lipschitz truncation for multi-phase problems

Improved phase distinction using Whitney decomposition

Enhanced analytical tools for degenerate parabolic equations

Abstract

This article is devoted to exploring the Lipschitz truncation method for parabolic multi-phase problems. The method is based on Whitney decomposition and covering lemmas with a delicate comparison scheme of appropriate alternatives to distinguish phases, as introduced by the first and the second author in [24].