Regularity in a one-phase free boundary problem for the fractional Laplacian

Details Regularity in a one-phase free boundary problem for the fractional Laplacian Regularity in a one-phase free boundary problem for the fractional Laplacian

2011-02-15

arxiv.org/abs/1102.3086v2

Mathematics

Analysis of PDEs

Corrected some typos

Scientific paper

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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