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Boundary Regularity for the Free Boundary in the One-phase Problem

Hector Chang-Lara, Columbia University
Tuesday, April 10, 2018 - 1:30pm to 3:30pm
PDL C-401

We consider the Bernoulli one-phase free boundary problem in a domain $\Omega$ and show that the free boundary F is C^{1,1/2} regular in a neighborhood of the fixed boundary $\partial \Omega$. We achieve this by relating the behavior of F near $\partial \Omega$ to a Signorini-type obstacle problem.