Free boundary regularity for the inhomogeneous one-phase Stefan problem

Abstract

In this paper, we prove that flat free boundaries of solutions to inhomogeneous one-phase Stefan problem are $C^{1,\hat{I}\pm }$. The method consists of employing a hodograph transform and deriving the regularity via a linearization technique, following the approach introduced by De Silva, Forcillo, and Savin in \cite{DFS23}.