Rocky Mountain Journal of Mathematics

Separability properties of singular degenerate abstract differential operators and applications

Veli B. Shakhmurov

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We study separability and spectral properties of singular degenerate elliptic equations in vector-valued $L_{p}$ spaces. We prove that a realization operator according to this equation with some boundary conditions is separable and Fredholm in $L_{p}$. The leading part of the associated differential operator is not self-adjoint. The sharp estimate of the resolvent, discreteness of spectrum and completeness of root elements of this operator is obtained. Moreover, we show that this operator is positive and generates a holomorphic $C_{0}$-semigroups on $L_{p}$. In application, we examine the regularity properties of nonlocal boundary value problem for degenerate elliptic equation and for the system of degenerate elliptic equations of either finite or infinite number.

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Rocky Mountain J. Math., Volume 49, Number 5 (2019), 1647-1666.

First available in Project Euclid: 19 September 2019

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separable differential operators spectral properties of differential operators degenerate differential equations abstract differential equations


Shakhmurov, Veli B. Separability properties of singular degenerate abstract differential operators and applications. Rocky Mountain J. Math. 49 (2019), no. 5, 1647--1666. doi:10.1216/RMJ-2019-49-5-1647.

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