For a one-phase free boundary problem involving a fractional Laplacian, we prove that “flat free boundaries” are . 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://www.numdam.org/articles/10.1016/j.anihpc.2011.11.003/} }
TY - JOUR AU - De Silva, D. AU - Roquejoffre, J.M. TI - Regularity in a one-phase free boundary problem for the fractional Laplacian JO - Annales de l'I.H.P. Analyse non linéaire PY - 2012 SP - 335 EP - 367 VL - 29 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.11.003/ DO - 10.1016/j.anihpc.2011.11.003 LA - en ID - AIHPC_2012__29_3_335_0 ER -
%0 Journal Article %A De Silva, D. %A Roquejoffre, J.M. %T Regularity in a one-phase free boundary problem for the fractional Laplacian %J Annales de l'I.H.P. Analyse non linéaire %D 2012 %P 335-367 %V 29 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2011.11.003/ %R 10.1016/j.anihpc.2011.11.003 %G en %F 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, 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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