A remark on nonlocal Neumann conditions for the fractional Laplacian

被引：10

作者：

Abatangelo, Nicola ^{[1
]}

机构：

[1] Goethe Univ Frankfurt Main, Inst Math, Robert Meyer Str 10, D-60325 Frankfurt, Germany

来源：

ARCHIV DER MATHEMATIK | 2020年 / 114卷 / 06期

关键词：

Fractional Laplacian; Nonlocal normal derivative; Nonlocal Neumann conditions; Regional Laplacian;

D O I：

10.1007/s00013-020-01440-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.

引用

页码：699 / 708

页数：10

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