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2019 Separability properties of singular degenerate abstract differential operators and applications
Veli B. Shakhmurov
Rocky Mountain J. Math. 49(5): 1647-1666 (2019). DOI: 10.1216/RMJ-2019-49-5-1647

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.

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Veli B. Shakhmurov. "Separability properties of singular degenerate abstract differential operators and applications." Rocky Mountain J. Math. 49 (5) 1647 - 1666, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1647

Information

Published: 2019
First available in Project Euclid: 19 September 2019

zbMATH: 07113703
MathSciNet: MR4010577
Digital Object Identifier: 10.1216/RMJ-2019-49-5-1647

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 5 • 2019
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