A one-phase problem for the fractional Laplacian: regularity of flat free boundaries
classification
🧮 math.AP
keywords
alphafreeboundariesflatfractionallaplacianone-phaseproblem
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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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