Parabolic Lipschitz truncation and Caloric Approximation

TL;DR

This paper introduces an improved parabolic Lipschitz truncation method that enhances control over time derivatives and boundary values, leading to a new caloric approximation lemma applicable to Orlicz growth settings.

Contribution

It presents a novel version of parabolic Lipschitz truncation with better qualitative control and extends caloric approximation to Orlicz growth environments.

Findings

Enhanced control of distributional time derivatives

Preservation of zero boundary values

Extension to Orlicz growth settings

Abstract

We develop an improved version of the parabolic Lipschitz truncation, which allows qualitative control of the distributional time derivative and the preservation of zero boundary values. As a consequence, we establish a new caloric approximation lemma. We show functions. The distance is measured in terms of spatial gradients as well as almost uniformly in time. Both results are extended to the setting of Orlicz growth.