Free boundary regularity for the inhomogeneous Stefan Problem

The Stefan problem describes the phenomenon of freezing and melting of a material with a solid-liquid interphase, such as ice and water. It can be formulated as a parabolic free boundary problem where the interface between the solid and the liquid regions evolves over time and is an unknown of the problem. After introducing the problem and some related literature, the seminar will focus on presenting some recent techniques to obtain regularity results starting from an initial suitable flatness assumption for the one-phase Stefan problem with the presence of a right-hand side. This talk will be based on a recent collaboration with F.Ferrari, N.Forcillo and D.Jesus.