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
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.
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.