ON APPROXIMATION OF THE SOLUTIONS OF BOUNDARY-VALUE PROBLEMS IN UNBOUNDED DOMAINS

Abstract

In this paper, it is proved that the solution of the boundary value problem in an unbounded domain $\Omega$ can be obtained as the limit as $r \rightarrow \infty$ of the solution u_r of the boundary value problem in a bounded domain $\Omega \cap \Omega B_ {r, \mu$, where $B_ {r, \mu}=\left\{x; \big |x \big |_\mu < r\right\}$ is a generalized ball. A similar result is obtained for solutions of problems in a half-space.