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 $C^\infty$ 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 a context is to establish estimates for the size of the singular set. The goal of this talk is to present some new results in this direction for the Stefan problem. This is a joint work with A. Figalli and J. Serra.

7 Oct 2022
4:00pm - 5:00pm
Where
https://hkust.zoom.us/j/99651193566 (Passcode: 615823)
Speakers/Performers
Prof. Xavier Ros-Oton
Universitat de Barcelona
Organizer(S)
Department of Mathematics
Contact/Enquiries
Payment Details
Audience
Alumni, Faculty and staff, PG students, UG students
Language(s)
English
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