Nonlocal elliptic problems and applications

ŞAHMUROV V.

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

  • Nəşrin Növü: Article / Article
  • Cild: 20 Say: 1
  • Nəşr tarixi: 2020
  • Doi nömrəsi: 10.17323/1609-4514-2020-20-1-185-210
  • jurnalın adı: Moscow Mathematical Journal
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Səhifə sayı: pp.185-210
  • Açar sözlər: Abstract Sobolev spaces, Differential-operator equation, Equations with variable coefficients, Nonlinear abstract differential equations, Separable boundary value problems, Well-posedness of parabolic problems
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

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.