Daniela De Silva, Ovidiu Savin, Yannick Sire
Published 2014-01-24Version 1
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 $\alpha=1/2.$
Comments: arXiv admin note: substantial text overlap with arXiv:1102.3086
Regularity in a one-phase free boundary problem for the fractional Laplacian
Regularity of flat free boundaries for a $p(x)$-Laplacian problem with right hand side
On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to Infinity
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