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

Tynysbek Sh. Kalmenov, Makhmud Abdysametovich Sadybekov, Berikbol T. Torebek

2018

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DOI 10.1080/17476933.2018.1437423

Data confidence 85 high

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Abstract

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.