Regularity of interfaces in phase transitions via obstacle problems
Analysis of PDEs
2018-09-24 v1
Abstract
The aim of this note is to review some recent developments on the regularity theory for the stationary and parabolic obstacle problems. After a general overview, we present some recent results on the structure of singular free boundary points. Then, we show some selected applications to the generic smoothness of the free boundary in the stationary obstacle problem (Schaeffer's conjecture), and to the smoothness of the free boundary in the one-phase Stefan problem for almost every time.
Cite
@article{arxiv.1809.02932,
title = {Regularity of interfaces in phase transitions via obstacle problems},
author = {Alessio Figalli},
journal= {arXiv preprint arXiv:1809.02932},
year = {2018}
}
Comments
Proceedings ICM 2018. arXiv admin note: text overlap with arXiv:1807.01193