On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem with surface tension

TL;DR

This paper investigates the smoothness of the moving boundary in a two-phase Stefan problem with surface tension, using advanced mathematical tools like diffeomorphisms, maximal regularity theory, and the implicit function theorem.

Contribution

It introduces a novel approach combining parameter-dependent diffeomorphisms and maximal regularity theory to analyze free boundary regularity in Stefan problems.

Findings

Established regularity results for the free boundary.

Developed a framework for analyzing interface smoothness.

Applied the implicit function theorem to free boundary problems.

Abstract

We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent diffeomorphisms, $L_p$-maximal regularity theory, and the implicit function theorem.