Rocky Mountain Journal of Mathematics

Separability properties of singular degenerate abstract differential operators and applications

Veli B. Shakhmurov

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 19 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1568880095

Digital Object Identifier
doi:10.1216/RMJ-2019-49-5-1647

Mathematical Reviews number (MathSciNet)
MR4010577

Zentralblatt MATH identifier
07113703

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

Citation

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. https://projecteuclid.org/euclid.rmjm/1568880095


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