International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 101-114
doi:10.1155/S0161171288000158

On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskij condition

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.