Electron. J. Differential Equations, Vol. 2016 (2016), No. 252, pp. 1-9.

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

Berikbol T. Torebek

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.


Submitted May 5, 2016. Published September 20, 2016.
Math Subject Classifications: 31A30, 31B30, 35J40.
Key Words: Elliptic equation; Robin-Cauchy problem; self-adjoint operator; ill-posedness.

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Berikbol T. Torebek
Department of Differential Equations
Department of Fundamental Mathematics
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhistan
email: torebek@math.kz

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