X. Ros-Oton | The singular set in the Stefan problem
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2022-08-01

O.A. Ladyzhenskaya centennial conference on PDE’s, St. Petersburg, July 16 – July 22, 2022
Xavier Ros-Oton (ICREA, Universitat de Barcelona)
The singular set in the Stefan problem

The Stefan problem, dating back to the XIXth century, is probably the most classical and important free boundary problem. The regularity of free boundaries in the Stefan problem was developed in the groundbreaking paper (Caffarelli, Acta Math. 1977). The main result therein establishes that the free boundary is 𝐶∞ in space and time, outside a certain set of singular points. The fine understanding of singularities is of central importance in a number of areas related to nonlinear PDEs and Geometric Analysis. In particular, a major question in such context is to establish estimates for the size of the singular set. The goal of this talk is to present new results in this direction for the Stefan problem in R^3. This is a joint work with A. Figalli and J. Serra.