Regular boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces

Angelo Favini, Veli Shakhmurov, Yakov Yakubov

Research output: Contribution to journalArticlepeer-review

Abstract

We consider coerciveness and Fredholmness of nonlocal boundary value problems for complete second order elliptic differential-operator equations in UMD Banach spaces. In some special cases, the main coefficients of the boundary conditions may be bounded operators and not only complex numbers. Then, we prove an isomorphism, in particular, maximal Lp-regularity, of the problem with a linear parameter in the equation. In both cases, the boundary conditions may also contain unbounded operators in perturbation terms. Finally, application to regular nonlocal boundary value problems for elliptic equations of the second order in non-smooth domains are presented. Equations and boundary conditions may contain differential-integral parts. The spaces of solvability are Sobolev type spaces Wp,q2,2.

Original languageEnglish
Pages (from-to)22-54
Number of pages33
JournalSemigroup Forum
Volume79
Issue number1
DOIs
StatePublished - Aug 2009

Keywords

  • Abstract elliptic equation
  • Elliptic boundary problem
  • Fredholmness
  • Isomorphism
  • R-sectorial operator
  • UMD Banach space

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