, Volume 46, Issue 3, pp 321-328
Date: 28 Apr 2010

On a nonlocal generalization of the biharmonic Dirichlet problem

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

Original Russian Text © G.K. Berikelashvili, D.G. Gordeziani, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 3, pp. 318–325.