Geodesic
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

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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.

@article{AIHPC_2012__29_3_335_0,
     author = {De Silva, D. and Roquejoffre, J.M.},
     title = {Regularity in a one-phase free boundary problem for the fractional {Laplacian}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {335--367},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     doi = {10.1016/j.anihpc.2011.11.003},
     zbl = {1251.35178},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.11.003/}
}
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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

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