arXiv subjects

Makhmud A. Sadybekov

Publications and source records attributed to Makhmud A. Sadybekov.

2 recordsLinked to original sources

arXiv2016

Some spectral properties and isoperimetric inequalities for a nonlocal Laplacian problem

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.

math.AP↗

arXiv2016

A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain

In this paper we consider the Cauchy problem for multidimensional elliptic equations in a cylindrical domain. The method of spectral expansion in eigenfunctions of the Cauchy problem for equations with deviating argument establishes a criterion of the strong solvability of the considered elliptic Cauchy problem. It is shown that the ill-posedness of the elliptic Cauchy problem is equivalent to the existence of an isolated point of the continuous spectrum for a self-adjoint operator with deviating argument.

math.AP↗