Some spectral properties and isoperimetric inequalities for a nonlocal Laplacian problem

Makhmud A. Sadybekov; Berikbol T. Torebek

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arXiv · 1608.05602

Some spectral properties and isoperimetric inequalities for a nonlocal Laplacian problem

Makhmud A. Sadybekov·Berikbol T. Torebek

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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.

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Makhmud A. Sadybekov, Berikbol T. Torebek. 2016-08-19. Some spectral properties and isoperimetric inequalities for a nonlocal Laplacian problem. https://arxiv.org/abs/1608.05602

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