Generic properties of eigenvalues of the fractional Laplacian

被引：2

作者：

Fall, Mouhamed Moustapha ^{[1
]}

Ghimenti, Marco ^{[2
]}

Micheletti, Anna Maria ^{[2
]}

Pistoia, Angela ^{[3
]}

机构：

[1] African Inst Math Sci Senegal, KM2 Route Joal Mbour 1418, Mbour, Senegal

[2] Univ Pisa, Dipartimento Matemat, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy

[3] Univ Roma La Sapienza, Dipartimento SBAI, via Antonio Scarpa 16, I-00161 Rome, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 08期

关键词：

VARIATIONAL ELLIPTIC OPERATOR;

D O I：

10.1007/s00526-023-02574-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Dirichlet eigenvalues of the fractional Laplacian (-Delta)(s), with s is an element of(0, 1), related to a smooth bounded domain Omega. We prove that there exists an arbitrarily small perturbation (Omega) over tilde = (I + psi)(Omega) of the original domain such that all Dirichlet eigenvalues of the fractional Laplacian associated to (Omega) over tilde are simple. As a consequence we obtain that all Dirichlet eigenvalues of the fractional Laplacian on an interval are simple. In addition, we prove that for a generic choice of parameters all the eigenvalues of some non-local operators are also simple.

引用

页数：17

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