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Algebra i Analiz, 2005, Volume 17, Issue 6, Pages 1–104 (Mi aa714)  

This article is cited in 105 scientific papers (total in 105 papers)

Expository Surveys

Averaging of periodic elliptic differential operators with the account of a corrector

M. Sh. Birman, T. A. Suslina

St. Petersburg State University, Faculty of Physics
References:
Received: 17.10.2005
English version:
St. Petersburg Mathematical Journal, 2006, Volume 17, Issue 6, Pages 897–973
DOI: https://doi.org/10.1090/S1061-0022-06-00935-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Sh. Birman, T. A. Suslina, “Averaging of periodic elliptic differential operators with the account of a corrector”, Algebra i Analiz, 17:6 (2005), 1–104; St. Petersburg Math. J., 17:6 (2006), 897–973
Citation in format AMSBIB
\Bibitem{BirSus05}
\by M.~Sh.~Birman, T.~A.~Suslina
\paper Averaging of periodic elliptic differential operators with the account of a~corrector
\jour Algebra i Analiz
\yr 2005
\vol 17
\issue 6
\pages 1--104
\mathnet{http://mi.mathnet.ru/aa714}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2202045}
\zmath{https://zbmath.org/?q=an:1175.35007}
\elib{https://elibrary.ru/item.asp?id=9188322}
\transl
\jour St. Petersburg Math. J.
\yr 2006
\vol 17
\issue 6
\pages 897--973
\crossref{https://doi.org/10.1090/S1061-0022-06-00935-6}
Linking options:
  • https://www.mathnet.ru/eng/aa714
  • https://www.mathnet.ru/eng/aa/v17/i6/p1
  • This publication is cited in the following 105 articles:
    1. Yi-Sheng Lim, Josip Žubrinić, “An Operator-Asymptotic Approach to Periodic Homogenization for Equations of Linearized Elasticity”, Asymptotic Analysis, 2025  crossref
    2. Kirill Cherednichenko, Alexander V. Kiselev, Igor Velčić, Josip Žubrinić, “Effective Behaviour of Critical-Contrast PDEs: Micro-Resonances, Frequency Conversion, and Time Dispersive Properties. II”, Commun. Math. Phys., 406:4 (2025)  crossref
    3. M. A. Dorodnyi, T. A. Suslina, “Porogovye approksimatsii funktsii ot faktorizovannogo operatornogo semeistva”, Algebra i analiz, 36:1 (2024), 95–161  mathnet
    4. T. A. Suslina, “Homogenization of elliptic and parabolic equations with periodic coefficients in a bounded domain under the Neumann condition”, Izv. Math., 88:4 (2024), 678–759  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. M. A. Dorodnyi, “High-frequency homogenization of multidimensional hyperbolic equations”, Applicable Analysis, 2024, 1  crossref
    6. S. E. Pastukhova, “Error estimates taking account of correctors in homogenization of elliptic operators”, Sb. Math., 215:7 (2024), 932–952  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. I. Y. Popov, E. S. Trifanova, A. S. Bagmutov, I. V. Blinova, “Barrier composed of perforated resonators and boundary conditions”, Eurasian Math. J., 15:3 (2024), 68–76  mathnet  crossref
    8. S. E. Pastukhova, “L2-otsenki pogreshnosti usredneniya parabolicheskikh uravnenii s uchetom korrektorov”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 134–151  mathnet  crossref
    9. S. E. Pastukhova, “On Operator Estimates of the Homogenization of Higher-Order Elliptic Systems”, Math. Notes, 114:3 (2023), 322–338  mathnet  crossref  crossref  mathscinet
    10. M. A. Dorodnyi, T. A. Suslina, “Homogenization of hyperbolic equations: operator estimates with correctors taken into account”, Funct. Anal. Appl., 57:4 (2023), 364–370  mathnet  crossref  crossref
    11. T. A. Suslina, “Operator-theoretic approach to the homogenization of Schrödinger-type equations with periodic coefficients”, Russian Math. Surveys, 78:6 (2023), 1023–1154  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. A. A. Raev, V. A. Slousch, T. A. Suslina, “Usrednenie odnomernogo periodicheskogo operatora chetvertogo poryadka s singulyarnym potentsialom”, Matematicheskie voprosy teorii rasprostraneniya voln. 53, Zap. nauchn. sem. POMI, 521, POMI, SPb., 2023, 212–239  mathnet
    13. A. A. Miloslova, T. A. Suslina, “Homogenization of the Higher-Order Parabolic Equations with Periodic Coefficients”, J Math Sci, 277:6 (2023), 959  crossref
    14. Andrii Khrabustovskyi, “Operator estimates for the Neumann sieve problem”, Annali di Matematica, 202:4 (2023), 1955  crossref
    15. Kirill Cherednichenko, Igor Velčić, Josip Žubrinić, “Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast”, Calc. Var., 62:5 (2023)  crossref
    16. V. A. Sloushch, T. A. Suslina, “Operator estimates for homogenization of higher-order elliptic operators with periodic coefficients”, St. Petersburg Math. J., 35:2 (2024), 327–375  mathnet  crossref
    17. T. A. Suslina, “Threshold approximations for the exponential of a factorized operator family with correctors taken into account”, St. Petersburg Math. J., 35:3 (2024), 537–570  mathnet  crossref
    18. Senik N.N., “Homogenization For Locally Periodic Elliptic Operators”, J. Math. Anal. Appl., 505:2 (2022), 125581  crossref  mathscinet  isi
    19. Dorodnyi M.A. Suslina T.A., “Homogenization of a Non-Stationary Periodic Maxwell System in the Case of Constant Permeability”, J. Differ. Equ., 307 (2022), 348–388  crossref  mathscinet  isi
    20. Cherednichenko K. D'Onofrio S., “Operator-Norm Homogenisation Estimates For the System of Maxwell Equations on Periodic Singular Structures”, Calc. Var. Partial Differ. Equ., 61:2 (2022), 67  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
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