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 Mat. Sb. (N.S.), 1984, Volume 125(167), Number 4(12), Pages 547–557 (Mi msb2100)

Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems

M. Ya. Spiridonov

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1986, 53:2, 551–561

Bibliographic databases:

UDC: 517.95
MSC: Primary 35J40; Secondary 35B99, 35J05

Citation: M. Ya. Spiridonov, “Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems”, Mat. Sb. (N.S.), 125(167):4(12) (1984), 547–557; Math. USSR-Sb., 53:2 (1986), 551–561

Citation in format AMSBIB
\Bibitem{Spi84} \by M.~Ya.~Spiridonov \paper Approximation of solutions of elliptic problems in domains with noncompact boundaries by solutions of exterior or interior problems \jour Mat. Sb. (N.S.) \yr 1984 \vol 125(167) \issue 4(12) \pages 547--557 \mathnet{http://mi.mathnet.ru/msb2100} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=770906} \zmath{https://zbmath.org/?q=an:0599.35054|0577.35032} \transl \jour Math. USSR-Sb. \yr 1986 \vol 53 \issue 2 \pages 551--561 \crossref{https://doi.org/10.1070/SM1986v053n02ABEH002956}