Regularity in a one-phase free boundary problem for the fractional Laplacian
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freeboundarylaplacianproblemfractionalone-phaseregularityalpha
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For a one-phase free boundary problem involving a fractional Laplacian, we prove that "flat free boundaries" are $C^{1,\alpha}$. We recover the regularity results of Caffarelli for viscosity solutions of the classical Bernoulli-type free boundary problem with the standard Laplacian.
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