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Mathematics of the USSR-Sbornik, 1977, Volume 32, Issue 2, Pages 227–244
DOI: https://doi.org/10.1070/SM1977v032n02ABEH002380
(Mi sm2810)
 

This article is cited in 68 scientific papers (total in 70 papers)

A boundary value problem for the second order elliptic equation in a domain with a narrow slit. 2. Domain with a small cavity

A. M. Il'in
References:
Received: 28.10.1976
Bibliographic databases:
UDC: 517.946.9
MSC: 35J25, 35B40
Language: English
Original paper language: Russian
Citation: A. M. Il'in, “A boundary value problem for the second order elliptic equation in a domain with a narrow slit. 2. Domain with a small cavity”, Math. USSR-Sb., 32:2 (1977), 227–244
Citation in format AMSBIB
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\by A.~M.~Il'in
\paper A~boundary value problem for the second order elliptic equation in a~domain with a~narrow slit. 2.~Domain with a~small cavity
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 2
\pages 227--244
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Linking options:
  • https://www.mathnet.ru/eng/sm2810
  • https://doi.org/10.1070/SM1977v032n02ABEH002380
  • https://www.mathnet.ru/eng/sm/v145/i2/p265
  • This publication is cited in the following 70 articles:
    1. D. B. Davletov, O. B. Davletov, R. R. Davletova, A. A. Ershov, “O sobstvennykh elementakh dvumernoi kraevoi zadachi tipa Steklova dlya operatora Lame”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:1 (2023), 54–65  mathnet  crossref  mathscinet
    2. D. B. Davletov, O. B. Davletov, R. R. Davletova, A. A. Ershov, “Skhodimost sobstvennykh elementov kraevoi zadachi tipa Steklova dlya operatora Lame”, Tr. IMM UrO RAN, 27, no. 1, 2021, 37–47  mathnet  crossref  elib
    3. D. I. Borisov, “Asimptoticheskii analiz kraevykh zadach dlya operatora Laplasa s chastoi smenoi tipa granichnykh uslovii”, Differentsialnye uravneniya s chastnymi proizvodnymi, SMFN, 67, no. 1, Rossiiskii universitet druzhby narodov, M., 2021, 14–129  mathnet  crossref
    4. Lucas Chesnel, Xavier Claeys, Sergei A. Nazarov, “Small obstacle asymptotics for a 2D semi-linear convex problem”, Applicable Analysis, 97:6 (2018), 962  crossref
    5. D. I. Borisov, A. I. Mukhametrakhimova, “The Norm Resolvent Convergence for Elliptic Operators in Multi-Dimensional Domains with Small Holes”, J Math Sci, 232:3 (2018), 283  crossref
    6. 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
    7. R. R. Gadyl'shin, S. V. Repjevskij, E. A. Shishkina, “On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 76–90  mathnet  crossref  mathscinet  isi  elib
    8. T. A. Mel'nik, G. A. Chechkin, “Eigenvibrations of thick cascade junctions with ‘very heavy’ concentrated masses”, Izv. Math., 79:3 (2015), 467–511  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. S. A. Nazarov, “Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube”, Trans. Moscow Math. Soc., 76:1 (2015), 1–53  mathnet  crossref  elib
    10. S. R. Garifullina, E. Yu. Postnikova, “Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes”, Comput. Math. Math. Phys., 53:11 (2013), 1591–1606  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    11. A. M. Il'in, S. V. Repjevskij, “On the Solvability of a Boundary-Value Problem for an Elliptic Equation”, Math. Notes, 92:2 (2012), 197–204  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    12. “Arlen Mikhailovich Ilin (k vosmidesyatiletiyu so dnya rozhdeniya)”, Ufimsk. matem. zhurn., 4:2 (2012), 3–12  mathnet  mathscinet
    13. A. R. Bikmetov, R. R. Gadylshin, “Vozmuschenie ellipticheskogo operatora uzkim potentsialom v n-mernoi oblasti”, Ufimsk. matem. zhurn., 4:2 (2012), 28–64  mathnet  mathscinet
    14. Postnikova E.Yu., “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 26, 49–58  mathscinet  elib
    15. E. Yu. Postnikova, “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik ChelGU, 2011, no. 13, 49–58  mathnet
    16. O. V. Izotova, S. A. Nazarov, G. Sweers, “Asymptotics of solutions and modeling of the Von Karman equations in a singularly perturbed domain”, J Math Sci, 173:5 (2011), 571  crossref
    17. Yu. N. Subbotin, N. I. Chernykh, “The Dirichlet problem in a domain with a slit”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S103–S117  mathnet  crossref  isi  elib
    18. S. A. Nazarov, “Asymptotic modeling of a problem with contrasting stiffness”, J. Math. Sci. (N. Y.), 167:5 (2010), 692–712  mathnet  crossref  elib
    19. Durante T., Kardone D., Nazarov S.A., “Modelirovanie sochlenenii plastin i sterzhnei posredstvom samosopryazhennykh rasshirenii”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 2, 3–14  zmath  elib
    20. D. B. Davletov, “Singularly perturbed Dirichlet boundary value problem for a stationary system in the linear elasticity theory”, Russian Math. (Iz. VUZ), 52:12 (2008), 4–12  mathnet  crossref  mathscinet  zmath  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    References:85
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