Geodesic
Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems
Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 551-561 
M. Ya. Spiridonov. Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems. Sbornik. Mathematics, Tome 53 (1986) no. 2, pp. 551-561. http://geodesic.mathdoc.fr/item/SM_1986_53_2_a15/
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     title = {Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems},
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     url = {http://geodesic.mathdoc.fr/item/SM_1986_53_2_a15/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\Omega^R$ ($R>0$) be a family of domains approximating a domain $\Omega^\infty$ as $R\to\infty$. For example, $\Omega^R$ can be a family of expanding domains whose union over all $R$ is $\Omega^\infty$, or a family of shrinking domains whose intersection is $\Omega^\infty$. Let $\mathfrak A_R$ be the operator corresponding to a formally symmetric elliptic boundary value problem in $\Omega^R$, and let $u_\varepsilon^R=(\mathfrak A_R+i\varepsilon)^{-1}f$. Conditions are determined under which $u_\varepsilon^R$ converges to a solution of the limit problem as $R\to\infty$, or as $\varepsilon\to0$ and $R\to\infty$ simultaneously. Figures: 2. Bibliography: 10 titles.

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