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

De Silva, D.; Roquejoffre, J.M.

doi:10.1016/j.anihpc.2011.11.003

De Silva, D. ; Roquejoffre, J.M.

Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 335-367.

Résumé

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.

Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2011.11.003

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     title = {Regularity in a one-phase free boundary problem for the fractional {Laplacian}},
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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://archive.numdam.org/articles/10.1016/j.anihpc.2011.11.003/

Bibliographie
Cité par

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