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

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.