Remarks on the spectrum of a non-local Dirichlet problem

被引：1

作者：

Benguria, Rafael D. ^{[1
]}

Pereira, Marcone C. ^{[2
]}

机构：

[1] Pontificia Univ Catolica Chile, Dept Fis, Casilla 306, Santiago 22, Chile

[2] IME Univ Sao Paulo, Dept Matemat Aplicada, Rua Matao 1010, Sao Paulo, SP, Brazil

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2021年 / 53卷 / 06期

基金：

巴西圣保罗研究基金会;

关键词：

45C05 (primary); 45A05 (secondary); INEQUALITIES;

D O I：

10.1112/blms.12552

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we analyse the spectrum of non-local Dirichlet problems with non-singular kernels in bounded open sets. The novelty is twofold. First we study the continuity of eigenvalues with respect to domain perturbation via Lebesgue measure. Next, under additional smooth conditions on the kernel and domain, we prove differentiability of simple eigenvalues computing their first derivative discussing extremum problems for eigenvalues.

引用

页码：1898 / 1915

页数：18

共 50 条

[21] A non-local semilinear eigenvalue problem
Franzina, Giovanni
Licheri, Danilo
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2022, 25 (06) : 2193 - 2221
[22] On a non-local problem for irregular equations
Kornienko, VV
[J]. SBORNIK MATHEMATICS, 2000, 191 (11-12) : 1607 - 1633
[23] A non-local semilinear eigenvalue problem
Giovanni Franzina
Danilo Licheri
[J]. Fractional Calculus and Applied Analysis, 2022, 25 : 2193 - 2221
[24] Remarks on entanglement measures and non-local state distinguishability
Eisert, J
Audenaert, K
Plenio, MB
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (20): : 5605 - 5615
[25] ESTIMATES OF HEAT KERNELS FOR NON-LOCAL REGULAR DIRICHLET FORMS
Grigor'yan, Alexander
Hu, Jiaxin
Lau, Ka-Sing
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (12) : 6397 - 6441
[26] Heat kernels and non-local Dirichlet forms on ultrametric spaces
Bendikov, Alexander
Grigor'yan, Alexander
Hu, Eryan
Hu, Jiaxin
[J]. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2021, 22 (01) : 399 - 461
[27] ON DUAL GENERATORS FOR NON-LOCAL SEMI-DIRICHLET FORMS
Uemura, Toshihiro
[J]. PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, 2014, 34 (02): : 199 - 214
[28] Non-perturbative spectrum of non-local gravity
Calcagni, Gianluca
Modesto, Leonardo
Nardelli, Giuseppe
[J]. PHYSICS LETTERS B, 2019, 795 : 391 - 397
[29] Elliptic Harnack inequalities for symmetric non-local Dirichlet forms
Chen, Zhen-Qing
Kumagai, Takashi
Wang, Jian
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 125 : 1 - 42
[30] A SIMPLE APPROACH TO FUNCTIONAL INEQUALITIES FOR NON-LOCAL DIRICHLET FORMS
Wang, Jian
[J]. ESAIM-PROBABILITY AND STATISTICS, 2014, 18 : 503 - 513

← 1 2 3 4 5 →