Some spectral properties and isoperimetric inequalities for a nonlocal Laplacian problem
Analysis of PDEs
2016-08-22 v1
Abstract
In this paper we consider a non-local problem for a Laplace operator in a multidimensional bounded symmetric domain. The investigated problem is an analogue of the classical periodic boundary value problems in the case of non-rectangular domain. We prove self-adjointness of the problem and show a method of constructing eigenfunctions. We obtain an analogue of the Rayleigh type inequality and some spectral inequalities for the first eigenvalue of the nonlocal problem.
Keywords
Cite
@article{arxiv.1608.05602,
title = {Some spectral properties and isoperimetric inequalities for a nonlocal Laplacian problem},
author = {Makhmud A. Sadybekov and Berikbol T. Torebek},
journal= {arXiv preprint arXiv:1608.05602},
year = {2016}
}
Comments
7 pages