Variational problems with free boundaries for the fractional Laplacian

• Autores: Luis A. Caffarelli, Jean-Michel Roquejoffre, Yannick Sire
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 12, Nº 5, 2010, págs. 1151-1179
• Idioma: inglés
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• Resumen

  • 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.