The Eigenvalue Problem for the Regional Fractional Laplacian in the Small Order Limit

被引：3

作者：

Temgoua, Remi Yvant ^{[1
,2
]}

Weth, Tobias ^{[1
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, Robert Mayer Str 10, D-60629 Frankfurt, Germany

[2] African Inst Math Sci Senegal AIMS Senegal, KM 2,Route Joal,BP 1418, Mbour, Senegal

来源：

POTENTIAL ANALYSIS | 2024年 / 60卷 / 01期

关键词：

Regional fractional Laplacian; Regional logarithmic Laplacian; Asymptotic behavior; Eigenfunctions; Eigenvalues;

D O I：

10.1007/s11118-022-10050-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we study the asymptotic behavior of eigenvalues and eigenfunctions of the regional fractional Laplacian (-Delta)(Omega)(s) as s -> 0(+). Our analysis leads to a study of the regional logarithmic Laplacian, which arises as a formal derivative of regional fractional Laplacians at s = 0.

引用

页码：285 / 306

页数：22

共 21 条

[1]

Andreu-Vaillo F., 2010, MATH SURVEYS MONOGRA

[2] Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling [J].