International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 101-113
doi:10.1155/S0161171288000158
On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskiĭ condition
The University of Queensland, Department of Mathematics, St. Lucia, 4067, Qld, Australia
Received 21 January 1987
Copyright © 1988 J. H. Chabrowski. 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
In this paper we investigate the solvability of a non-local problem for a linear elliptic equation, which is also known as the boundary value problem with the Bitsadze-Samarskiĭ condition. We prove the existence and uniqueness of a classical solution to this problem. In the final part of this paper we propose an L2-approach which gives a rise to weak solutions in a weighted Sobolev space. The crucial point in proving the existence of weak solutions is a suitable modification of the Bitsadze-Samarskiĭ condition.