Remarks on the spectrum of a non-local Dirichlet problem

Full text
Author(s):	Benguria, Rafael D. ^[1] ; Pereira, Marcone C. ^[2] Total Authors: 2
Affiliation:	^[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 Total Affiliations: 2
Document type:	Journal article
Source:	BULLETIN OF THE LONDON MATHEMATICAL SOCIETY; v. 53, n. 6 NOV 2021.
Web of Science Citations:	0
Abstract
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. (AU)

FAPESP's process:	19/06221-5 - Spectral analysis of linear operators given by nonlocal model for dispersion and diffusion
Grantee:	Marcone Corrêa Pereira
Support Opportunities:	Scholarships abroad - Research