Regularity in a one-phase free boundary problem for the fractional Laplacian
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 335-367.

For a one-phase free boundary problem involving a fractional Laplacian, we prove that “flat free boundaries” are C 1,α . 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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     title = {Regularity in a one-phase free boundary problem for the fractional {Laplacian}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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De Silva, D.; Roquejoffre, J.M. Regularity in a one-phase free boundary problem for the fractional Laplacian. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 335-367. doi : 10.1016/j.anihpc.2011.11.003. http://www.numdam.org/articles/10.1016/j.anihpc.2011.11.003/

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