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

  • Nəşrin Növü: Article / Article
  • Cild: 49 Say: 5
  • Nəşr tarixi: 2019
  • Doi nömrəsi: 10.1216/rmj-2019-49-5-1647
  • jurnalın adı: Rocky Mountain Journal of Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.1647-1666
  • Açar sözlər: Abstract differential equations, Degenerate differential equations, Separable differential operators, Spectral properties of differential operators
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

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.