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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 6, Pages 1322–1339 (Mi izv1466)  

This article is cited in 1 scientific paper (total in 3 paper)

The asymptotics of the Green function for a second-order elliptic equation near the boundary of the domain

A. M. Il'in, B. I. Suleimanov


Abstract: The Green function $G(x,\xi)$ of the first boundary value problem in a bounded domain with smooth boundary is investigated. It is assumed that the point $\xi$, where the function has a singularity, tends to the boundary of the domain. Under this condition an asymptotic expansion of $G(x,\xi)$ is constructed up to any power of the distance from $\xi$ to the boundary. Asymptotic expansions different in form are constructed for points $x$ near $\xi$ and for points far from $\xi$. The final construction and the justification for the asymptotics of $G(x,\xi)$ is carried out by the method of matching asymptotic expansions.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:3, 579–594

Bibliographic databases:

UDC: 517.946
MSC: Primary 35J25; Secondary 41A60
Received: 05.10.1981

Citation: A. M. Il'in, B. I. Suleimanov, “The asymptotics of the Green function for a second-order elliptic equation near the boundary of the domain”, Izv. Akad. Nauk SSSR Ser. Mat., 47:6 (1983), 1322–1339; Math. USSR-Izv., 23:3 (1984), 579–594

Citation in format AMSBIB
\Bibitem{IliSul83}
\by A.~M.~Il'in, B.~I.~Suleimanov
\paper The asymptotics of the Green function for a~second-order elliptic equation near the boundary of the domain
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 6
\pages 1322--1339
\mathnet{http://mi.mathnet.ru/izv1466}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=727758}
\zmath{https://zbmath.org/?q=an:0599.35044}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 3
\pages 579--594
\crossref{https://doi.org/10.1070/IM1984v023n03ABEH001787}


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    This publication is cited in the following articles:
    1. V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S1–S7  mathnet  mathscinet  zmath  elib
    2. “Arlen Mikhailovich Ilin (k vosmidesyatiletiyu so dnya rozhdeniya)”, Ufimsk. matem. zhurn., 4:2 (2012), 3–12  mathnet  mathscinet
    3. S. F. Dolbeeva, V. N. Pavlenko, S. V. Matveev, O. N. Dementev, A. V. Melnikov, E. A. Sbrodova, A. A. Solovev, V. I. Ukhobotov, V. E. Fedorov, E. A. Fominykh, A. A. Ershov, “Arlen Mikhailovich Ilin. 85 let so dnya rozhdeniya”, Chelyab. fiz.-matem. zhurn., 2:1 (2017), 5–9  mathnet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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