Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
Volume 12, Issue 5, Pages 1151-1179Publisher
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JEMS/226
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Funding
- INSA of Toulouse
- University of Texas
- Institut Universitaire de France
- University of Texas at Austin
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We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.
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