Differential Equations

, Volume 46, Issue 3, pp 321–328

On a nonlocal generalization of the biharmonic Dirichlet problem

  • G. K. Berikelashvili
  • D. G. Gordeziani
Partial Differential Equations

DOI: 10.1134/S001226611003002X

Cite this article as:
Berikelashvili, G.K. & Gordeziani, D.G. Diff Equat (2010) 46: 321. doi:10.1134/S001226611003002X

Abstract

We consider a mixed problem with the Dirichlet boundary conditions and integral conditions for the biharmonic equation. We prove the existence and uniqueness of a generalized solution in the weighted Sobolev space W22. We show that the problem can be viewed as a generalization of the Dirichlet problem.

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • G. K. Berikelashvili
    • 1
    • 2
  • D. G. Gordeziani
    • 1
    • 2
  1. 1.Razmadze Mathematical InstituteTbilisiGeorgia
  2. 2.Vekua Institute of Applied MathematicsTbilisi State UniversityTbilisiGeorgia