ON APPROXIMATION OF THE SOLUTIONS OF BOUNDARY-VALUE PROBLEMS IN UNBOUNDED DOMAINS - Dallakyan, G. V. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2000)
In this paper, it is proved that the solution of the boundary value problem in an unbounded domain $Ω$ can be obtained as the limit as $r → ∞$ of the solution ur of the boundary value problem in a bounded domain $Ω \cap Ω B_ {r, μ$, where $B_ {r, μ}=\left\{x; \big |x \big |_μ < r\right\}$ is a generalized ball. A similar result is obtained for solutions of problems in a half-space.
Keywords: boundary value problem; an unbounded domain; half-space