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Boundary Regularity for the Free Boundary in the One-phase Problem (1709.03371v1)
Published 11 Sep 2017 in math.AP
Abstract: 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.
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