Speaker
Giacomo Colombo
(ETH Zürich)
Description
The Stefan problem describes the evolution of phase transitions, such as ice melting into water. In this talk, we will discuss the fine structure of the singular set of the free boundary. More precisely, we recently proved that, outside an $(n-2)$-dimensional set, the singular part is contained in an $(n-1)$-dimensional manifold of class $C^\infty$. We will first describe this result and explain its implications for the generic-in-time regularity of free boundaries in low dimensions. Then, we will present recent joint work with Alessio Figalli showing that, for a generic solution, the whole singular set has parabolic dimension at most $n-2$.
Author
Giacomo Colombo
(ETH Zürich)