Regularity theory for elliptic and parabolic free boundary problems

点击翻译按钮获取中文摘要

The main objective of the proposal is to establish the regularity of solutions and free boundaries for free boundary problems. In particular, we focus on such problems which can be formulated as obstacle or Stefan type problems. Typically the problems we consider are evolutionary, or partially degenerate, or nonlocal, such that certain standard tools for the model problems are not available or hard to implement. We aim to develop new methods to treat the regularity and the long time asymptotics of solutions, and also to understand how degeneracy or nonlocal effects influence the behavior of the free boundaries.