Electronic Journal of Differential Equations (Sep 2016)

A method for solving ill-posed Robin-Cauchy problems for second-order elliptic equations in multi-dimensional cylindrical domains

  • Berikbol T. Torebek

Journal volume & issue
Vol. 2016, no. 252,
pp. 1 – 9

Abstract

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

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