Generalized principal eigenvalues on $\mathbb{R}^d$ of second order elliptic operators with rough nonlocal kernels
Analysis of PDEs
2022-11-24 v4 Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2010.12952,
title = {Generalized principal eigenvalues on $\mathbb{R}^d$ of second order elliptic operators with rough nonlocal kernels},
author = {Ari Arapostathis and Anup Biswas and Prasun Roychowdhury},
journal= {arXiv preprint arXiv:2010.12952},
year = {2022}
}
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23 pages