Title
One-Phase Free Boundary Problems on Riemannian Complexes
Abstract
Free boundary problems model situations where an unknown interface is part of the solution. A typical case involves minimizers of the Bernoulli functional, whose positivity set defines the free boundary. While well understood on smooth cases, much less is known for singular spaces.
In this talk, we consider one-phase free boundary problems on admissible piecewise smooth Riemannian complexes, focusing on the existence, regularity, and geometry of minimizers and free boundaries. This is based on a joint work with Hui-Chun Zhang and Xi-Ping Zhu.
