The EMS Publishing House is now EMS Press and has its new home at ems.press.
Please find all EMS Press journals and articles on the new platform.
Journal of the European Mathematical Society
Full-Text PDF (266 KB) | Metadata |
Table of Contents | JEMS summary
Published online: 2010-08-15
Variational problems with free boundaries for the fractional Laplacian
Luis A. Caffarelli[1], Jean-Michel Roquejoffre[2] and Yannick Sire[3] (1) University of Texas at Austin, USA(2) Université Paul Sabatier, Toulouse, France
(3) Université Aix-Marseille, Marseille, France
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.
Keywords: Fractional Laplacian, free boundary
Caffarelli Luis, Roquejoffre Jean-Michel, Sire Yannick: Variational problems with free boundaries for the fractional Laplacian. J. Eur. Math. Soc. 12 (2010), 1151-1179. doi: 10.4171/JEMS/226