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

Published 24 Jan 2014 in math.AP | (1401.6443v1)

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 $\alpha=1/2.$

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