One-phase Free Boundary Problems

Sunday, May 31, 2015 - 9:00am - 9:50am
Lind 305
Daniela De Silva (Columbia University)
In this talk we will provide an overview of the regularity theory for a one-phase (Bernoulli) free boundary problem. We will describe several results which parallel the regularity theory of minimal surfaces, including flatness theorems, monotonicity formulae, regularity in low dimensions, a priori gradient bounds. We will then talk about the thin one-phase problem, that can be viewed as a non-local version of the classical one-phase problem. We will highlight the differences in the strategy developed to investigate regularity issues with respect to the classical case.