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Algebra i Analiz, 2003, Volume 15, Issue 5, Pages 1–108 (Mi aa817)  

This article is cited in 199 scientific papers (total in 199 papers)

Expository Surveys

Periodic differential operators of second order. Threshold properties and averagings

M. Sh. Birman, T. A. Suslina

St. Petersburg State University, Faculty of Physics
References:
Received: 25.06.2003
English version:
St. Petersburg Mathematical Journal, 2004, Volume 15, Issue 5, Pages 639–714
DOI: https://doi.org/10.1090/S1061-0022-04-00827-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Sh. Birman, T. A. Suslina, “Periodic differential operators of second order. Threshold properties and averagings”, Algebra i Analiz, 15:5 (2003), 1–108; St. Petersburg Math. J., 15:5 (2004), 639–714
Citation in format AMSBIB
\Bibitem{BirSus03}
\by M.~Sh.~Birman, T.~A.~Suslina
\paper Periodic differential operators of second order. Threshold properties and averagings
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 5
\pages 1--108
\mathnet{http://mi.mathnet.ru/aa817}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2068790}
\zmath{https://zbmath.org/?q=an:1072.47042}
\transl
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 5
\pages 639--714
\crossref{https://doi.org/10.1090/S1061-0022-04-00827-1}
Linking options:
  • https://www.mathnet.ru/eng/aa817
  • https://www.mathnet.ru/eng/aa/v15/i5/p1
  • This publication is cited in the following 199 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. Nikolay Filonov, Ilya Kachkovskiy, “On Spectral Bands of Discrete Periodic Operators”, Commun. Math. Phys., 405:2 (2024)  crossref
    5. Kirill D. Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev, “Norm-Resolvent Convergence for Neumann Laplacians on Manifold Thinning to Graphs”, Mathematics, 12:8 (2024), 1161  crossref
    6. 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
    7. Alexander V. Kiselev, Kirill Ryadovkin, “Phase Transition in a Periodic Tubular Structure”, SIAM J. Appl. Math., 84:3 (2024), 890  crossref
    8. K. S. Ryadovkin, “On periodic branching random walks on Zd with infinite variance of jumps”, Theory Probab. Appl., 69:1 (2024), 88–98  mathnet  crossref  crossref
    9. Yi-Sheng Lim, “A high-contrast composite with annular inclusions: Norm-resolvent asymptotics”, Journal of Mathematical Analysis and Applications, 539:1 (2024), 128462  crossref
    10. M. A. Dorodnyi, “High-frequency homogenization of multidimensional hyperbolic equations”, Applicable Analysis, 2024, 1  crossref
    11. 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
    12. M. V. Platonova, K. S. Ryadovkin, “Vetvyaschiesya diffuzionnye protsessy v periodicheskikh sredakh”, Veroyatnost i statistika. 36, Zap. nauchn. sem. POMI, 535, POMI, SPb., 2024, 214–236  mathnet
    13. S. A. Nazarov, “Asimptotika spektra kraevoi zadachi s usloviem Steklova na melkikh mnozhestvakh, raspredelënnykh periodicheski vdol kontura”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 51, K yubileyu Niny Nikolaevny Uraltsevoi, Zap. nauchn. sem. POMI, 536, POMI, SPb., 2024, 178–227  mathnet
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. D.I. Borisov, “Homogenization for operators with arbitrary perturbations in coefficients”, Journal of Differential Equations, 369 (2023), 41  crossref
    20. Éric Cancès, Louis Garrigue, David Gontier, “Second-Order Homogenization of Periodic Schrödinger Operators with Highly Oscillating Potentials”, SIAM J. Math. Anal., 55:3 (2023), 2288  crossref
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