Separability properties of singular degenerate abstract differential operators and applications

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ŞAHMUROV V.

Rocky Mountain Journal of Mathematics, vol.49, no.5, pp.1647-1666, 2019 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.1216/rmj-2019-49-5-1647
  • Journal Name: Rocky Mountain Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1647-1666
  • Keywords: Abstract differential equations, Degenerate differential equations, Separable differential operators, Spectral properties of differential operators
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

We study separability and spectral properties of singular degenerate elliptic equations in vector-valued Lp spaces. We prove that a realization operator according to this equation with some boundary conditions is separable and Fredholm in Lp. 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 C0-semigroups on Lp. 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.