The one-phase Stefan problem: a perturbative approach for the free boundary regularity

Date: 2022-11-08

Time: 15:00 - 16:00


Nicolo Forcillo


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.