Geodesic
Variational problems with free boundaries for the fractional Laplacian
Journal of the European Mathematical Society, Tome 12 (2010) no. 5, pp. 1151-1179.

Voir la notice de l'article provenant de 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.
DOI : 10.4171/jems/226
Classification : 35-XX, 00-XX
Keywords: Fractional Laplacian, free boundary 
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     title = {Variational problems with free boundaries for the fractional {Laplacian}},
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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. http://geodesic.mathdoc.fr/articles/10.4171/jems/226/

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