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

[1] Remarks on a non-local boundary value problem
Webb, J. R. L.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (02) : 1075 - 1077
[2] Dirichlet problem for an equation of non-local diffusion with source
Bogoya, Mauricio
Maricel Elorreaga, Luz
[J]. BOLETIN DE MATEMATICAS, 2012, 19 (01): : 55 - 64
[3] SOME REMARKS ON THE MASS SPECTRUM AND NON-LOCAL INTERACTION
GOTO, H
[J]. PROGRESS OF THEORETICAL PHYSICS, 1953, 10 (06): : 698 - 700
[4] Numerical solution of the Dirichlet problem with non-local boundary conditions
Dautov, RZ
Sarimov, NN
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1995, 35 (09) : 1089 - 1102
[5] REMARKS ON THE NON-LOCAL ELECTRODYNAMICS
RAYSKI, J
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1951, 206 (1087): : 575 - 583
[6] LOCAL AND NON-LOCAL DIRICHLET FORMS ON THE SIERPITSKI CARPET
Grigor'yan, Alexander
Yang, Meng
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (06) : 3985 - 4030
[7] REMARKS ON NON-LOCAL SPINOR FIELD
YUKAWA, H
[J]. PHYSICAL REVIEW, 1949, 76 (11): : 1731 - 1731
[8] Isoperimetric Inequalities for Non-Local Dirichlet Forms
Wang, Feng-Yu
Wang, Jian
[J]. POTENTIAL ANALYSIS, 2020, 53 (04) : 1225 - 1253
[9] Isoperimetric Inequalities for Non-Local Dirichlet Forms
Feng-Yu Wang
Jian Wang
[J]. Potential Analysis, 2020, 53 : 1225 - 1253
[10] Various approaches to the Dirichlet problem for non-local operators satisfying the positive maximum principle
Jacob, N
[J]. POTENTIAL THEORY - ICPT 94, 1996, : 367 - 375

← 1 2 3 4 5 →