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

Abstract

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.

Keywords

• Elliptic equation
• Robin-Cauchy problem
• self-adjoint operator
• ill-posedness