Differential Equations

, Volume 46, Issue 3, pp 321–328 | Cite as

On a nonlocal generalization of the biharmonic Dirichlet problem

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


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 W 2 2 . We show that the problem can be viewed as a generalization of the Dirichlet problem.


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© 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

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