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arXiv · 1401.6443

A one-phase problem for the fractional Laplacian: regularity of flat free boundaries

Daniela De Silva·Ovidiu Savin·Yannick Sire
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Abstract

We consider a one-phase free boundary problem involving a fractional Laplacian $(-Δ)^α$, $0<α<1,$ and we prove that ``flat free boundaries" are $C^{1,γ}$. We thus extend the known result for the case $α=1/2.$

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Daniela De Silva, Ovidiu Savin, Yannick Sire. 2014-01-24. A one-phase problem for the fractional Laplacian: regularity of flat free boundaries. https://arxiv.org/abs/1401.6443

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