# Nicolò Forcillo: The one-phase Stefan problem: a pertubative approach for the free boundary regularity

**Time: **
Tue 2022-11-08 15.00 - 16.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

**Video link: **
Meeting ID: 921 756 1880

**Participating: **
Nicolò Forcillo - University of Bologna

**Abstract:**

In Stefan type problems, free boundaries may not regularize instantaneously. In particular, there exist examples in which Lipschitz free boundaries preserve corners. Nevertheless, in the two-phase Stefan problem, I. Athanasopoulos, L. Caffarelli, and S. Salsa showed that Lipschitz free boundaries in space-time become smooth under a nondegeneracy condition, as well as sufficiently ""flat"" ones. Their techniques are based on the original work of Caffarelli in the elliptic case. In the talk, we present a more recent approach to investigate the regularity of flat free boundaries for the one-phase Stefan problem. Specifically, it relies on perturbation arguments leading to a linearization of the problem, in the spirit of the elliptic counterpart already developed by D. De Silva. This talk is based on a joint work with D. De Silva and O. Savin.