Generalized principal eigenvalues on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^{d}$$\end{document} of second order elliptic operators with rough nonlocal kernels

被引：0
作者：
Ari Arapostathis
Anup Biswas
Prasun Roychowdhury
机构：
[1] The University of Texas at Austin,Department of ECE
[2] Indian Institute of Science Education and Research,Department of Mathematics
来源：
Nonlinear Differential Equations and Applications NoDEA | 2023年 / 30卷 / 1期
关键词：
Principal eigenvalue; Nonlocal operators; Maximum principle; Simple eigenvalue; Harnack inequality; Primary 35P30; 35B50;
D O I：
10.1007/s00030-022-00821-z
中图分类号：
学科分类号：
摘要：
We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for singular kernels. The first part of the paper presents results concerning the existence of a principal eigenfunction. Then we present various necessary and/or sufficient conditions for the maximum principle to hold, and use these to characterize the simplicity of the principal eigenvalue.
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