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arXiv · 1102.3086

Regularity in a one-phase free boundary problem for the fractional Laplacian

Daniela De Silva·Jean-Michel Roquejoffre
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Abstract

For a one-phase free boundary problem involving a fractional Laplacian, we prove that "flat free boundaries" are $C^{1,\alpha}$. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian.

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Daniela De Silva, Jean-Michel Roquejoffre. 2011-02-15. Regularity in a one-phase free boundary problem for the fractional Laplacian. https://doi.org/10.1016/j.anihpc.2011.11.003

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