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arXiv · 1512.00917

Regularity of the Free Boundary for a Bernoulli-Type Parabolic Problem with Variable Coefficients

Thomas Backing
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Abstract

This paper studies the regularity of the free boundary for viscosity solutions to a parabolic Bernoulli-type free boundary problem with variable coefficients. The main result is that Lipschitz free boundaries are $C^1$ with a normal vector that varies with a Hölder modulus of continuity in both space and in time. As a consequence, the viscosity solution satisfies the free boundary problem in a classical sense.

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Thomas Backing. 2015-12-03. Regularity of the Free Boundary for a Bernoulli-Type Parabolic Problem with Variable Coefficients. https://arxiv.org/abs/1512.00917

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