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Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 93858, 6 pages
doi:10.1155/JIA/2006/93858

To a nonlocal generalization of the Dirichlet problem

Givi Berikelashvili

A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1 M. Aleksidze Street, Tbilisi, Georgia 0193, Caucasus, USA

Received 20 August 2004; Accepted 22 September 2004

Abstract

A mixed problem with a boundary Dirichlet condition and nonlocal integral condition is considered for a two-dimensional elliptic equation.The existence and uniqueness of a weak solution of this problem are proved in a weighted Sobolev space.