Variational problems with free boundaries for the fractional Laplacian
Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1151-1179
Cet article a éte moissonné depuis la source EMS Press
We discuss properties (optimal regularity, non-degeneracy, smoothness of the free boundary...) of a variational interface problem involving the fractional Laplacian; Due to the non-locality of the Dirichlet problem, the task is nontrivial. This difficulty is by-passed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a co-dimension 2 (degenerate) free boundary.
@article{JEMS_2010_12_5_a3,
author = {Luis A. Caffarelli and Jean-Michel Roquejoffre and Yannick Sire},
title = {Variational problems with free boundaries for the fractional {Laplacian}},
journal = {Journal of the European Mathematical Society},
pages = {1151--1179},
year = {2010},
volume = {12},
number = {5},
doi = {10.4171/jems/226},
url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/226/}
}
TY - JOUR AU - Luis A. Caffarelli AU - Jean-Michel Roquejoffre AU - Yannick Sire TI - Variational problems with free boundaries for the fractional Laplacian JO - Journal of the European Mathematical Society PY - 2010 SP - 1151 EP - 1179 VL - 12 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4171/jems/226/ DO - 10.4171/jems/226 ID - JEMS_2010_12_5_a3 ER -
%0 Journal Article %A Luis A. Caffarelli %A Jean-Michel Roquejoffre %A Yannick Sire %T Variational problems with free boundaries for the fractional Laplacian %J Journal of the European Mathematical Society %D 2010 %P 1151-1179 %V 12 %N 5 %U http://geodesic.mathdoc.fr/articles/10.4171/jems/226/ %R 10.4171/jems/226 %F JEMS_2010_12_5_a3
Luis A. Caffarelli; Jean-Michel Roquejoffre; Yannick Sire. Variational problems with free boundaries for the fractional Laplacian. Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1151-1179. doi: 10.4171/jems/226
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