Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 93858, 6 pages

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

Copyright © 2006 Givi Berikelashvili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.