Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
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DOI：
10.1007/s00222-007-0086-6
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发表时间：
2008-02-01
影响因子：
3.1
通讯作者：
Silvestre, Luis
中科院分区：
文献类型：
--
作者：
Caffarelli, Luis A.;Salsa, Sandro;Silvestre, Luis
我们利用分数阶拉普拉斯算子作为一个适当微分方程的狄氏 - 诺伊曼算子的一种刻画来研究其障碍问题。我们将其写成一个等价的刻画，作为一个薄障碍问题。通过这种方式，我们能够应用局部型的论证来获得解的精确正则性估计，并研究自由边界的正则性。
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary.