Mathematics

On some spectral properties of a class of degenerate elliptic differential operators

S. A. Iskhokov^ab, M. G. Gadoev^b, M. N. Petrova<sup>b

a</sup> Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe
^b Mirnyi Polytechnic Institute (branch of the North-Eastern Federal University in Mirnyi)

Abstract: Some spectral properties are investigated for a class of degenerate-elliptic operators A with singular matrix coefficients generated by noncoercive sesquilinear forms. Operator A is considered in the Hilbert space $L_2(\Omega)^l$, where $\Omega\subset R^n$ is a limit-tube domain and $l>0$ is an integer.

Keywords: spectral properties, degenerate-elliptic operator, noncoercitive sesquilinear form, limit-cylindrical $(x)$ domain, resolvent of generalized Dirichlet problem.

UDC: 517.918+516.918

Received: 14.01.2016

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