|Location:||MSRI: Simons Auditorium|
We will discuss an Alt-Caffarelli-Friedman type variational problem that exhibits a codimension two free boundary. We will show the optimal regularity, nondegeneracy, among other things, as well as a new phenomenon that the positive and negative phases are always separated. We will then discuss the regularity of the free boundary in dimension 3 by using Alexandrov's reflection comparison technique.
Based on a joint work with Mark Allen.No Notes/Supplements Uploaded No Video Files Uploaded