Variational problems with free boundaries for the fractional Laplacian
Variational problems with free boundaries for the fractional Laplacian
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DOI：
10.4171/jems/226
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发表时间：
2010-08
影响因子：
2.6
通讯作者：
L. Caffarelli;J. Roquejoffre;Y. Sire
中科院分区：
文献类型：
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作者：
L. Caffarelli;J. Roquejoffre;Y. Sire
我们讨论了一些性质(自由边界的最佳正则性、非简并性、光滑性……)关于涉及分数次拉普拉斯的变分界面问题由于狄利克雷问题的非局部性，该任务是非平凡的。第一作者和Silvestre发现的一个推广公式绕过了这一困难，该公式将研究简化为余维2(简并)自由边界的研究。
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.