A replacement lemma for obtaining pointwise estimates in phase transition models

TL;DR

This paper introduces a novel replacement lemma for variational problems that enables deriving pointwise estimates in phase transition models without relying on local arguments.

Contribution

The paper presents a new replacement lemma applicable to variational problems, facilitating pointwise estimates in phase transition models through a non-local approach.

Findings

Established a replacement lemma for variational problems.

Applied the lemma to phase transition models to obtain pointwise estimates.

Demonstrated the effectiveness of the non-local approach in this context.

Abstract

We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.