Semigroup Forum

, Volume 79, Issue 1, pp 22–54

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

Research Article

DOI: 10.1007/s00233-009-9138-0

Cite this article as:
Favini, A., Shakhmurov, V. & Yakubov, Y. Semigroup Forum (2009) 79: 22. doi:10.1007/s00233-009-9138-0

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.

Keywords

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

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversita di BolognaBolognaItaly
  2. 2.Department of Mathematics AkfiratOkan UniversityTuzlaTurkey
  3. 3.Raymond and Beverly Sackler School of Mathematical SciencesTel-Aviv UniversityTel-AvivIsrael