Regularity of the free boundary in the one-phase Stefan problem: a recent approach

Abstract

In this note, we discuss about the regularity of the free boundary for the solutions of the one-phase Stefan problem. We start by recalling the classical results achieved by I. Athanasopoulos, L. Caffarelli, and S. Salsa in the more general setting of the two-phase Stefan problem. Next, we focus on some recent achievements on the subject, obtained with Daniela De Silva and Ovidiu Savin starting from the techniques already known for one-phase problems governed by elliptic operators.