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

Abstract

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

arXiv admin note: substantial text overlap with arXiv:1102.3086

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