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

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.

@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},
publisher = {Elsevier},
volume = {29},
number = {3},
year = {2012},
pages = {335-367},
doi = {10.1016/j.anihpc.2011.11.003},
zbl = {1251.35178},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2012__29_3_335_0}
}

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, Volume 29 (2012) no. 3, pp. 335-367. doi : 10.1016/j.anihpc.2011.11.003. http://www.numdam.org/item/AIHPC_2012__29_3_335_0/

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