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arXiv · 1709.03371

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

Hector Chang-Lara·Ovidiu Savin
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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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Hector Chang-Lara, Ovidiu Savin. 2017-09-11. Boundary Regularity for the Free Boundary in the One-phase Problem. https://arxiv.org/abs/1709.03371

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