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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 302628, 4 pages
http://dx.doi.org/10.1155/2013/302628
Research Article

The Dirichlet Problem for the Equation in the Exterior of Nonclosed Lipschitz Surfaces

KIAM, Miusskaya Sq. 4, Moscow 125047, Russia

Received 20 March 2012; Accepted 7 September 2012

Academic Editor: Attila Gilányi

Copyright © 2013 P. A. Krutitskii. 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

We study the Dirichlet problem for the equation in the exterior of nonclosed Lipschitz surfaces in . The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable.