Nonlocal elliptic problems and applications

ŞAHMUROV V.

Moscow Mathematical Journal, vol.20, no.1, pp.185-210, 2020 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.17323/1609-4514-2020-20-1-185-210
  • Journal Name: Moscow Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.185-210
  • Keywords: Abstract Sobolev spaces, Differential-operator equation, Equations with variable coefficients, Nonlinear abstract differential equations, Separable boundary value problems, Well-posedness of parabolic problems
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

In this paper, the integral boundary value problems for differential-operator equations with principal variable coefficients are studied. Several conditions for the Lp-separability are given. Moreover, the sharp coercive estimates for resolvents of corresponding differential operators are shown. It is implied that these operators are positive and also are generators of analytic semigroups. Then, the existence and uniqueness of maximal regular solution to nonlinear abstract elliptic equations is derived. In application, maximal regularity properties of the abstract parabolic equation with variable coefficients and systems of elliptic equations are derived in mixed Lp-spaces.