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Algebra i Analiz, 2003, Volume 15, Issue 4, Pages 61–71 (Mi aa800)  

This article is cited in 41 scientific papers (total in 41 papers)

Research Papers

Average procedure for periodic operators near an edge of internal gap

M. Sh. Birman

St. Petersburg State University, Faculty of Physics
References:
Received: 02.06.2003
English version:
St. Petersburg Mathematical Journal, 2004, Volume 15, Issue 4, Pages 507–513
DOI: https://doi.org/10.1090/S1061-0022-04-00819-2
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Sh. Birman, “Average procedure for periodic operators near an edge of internal gap”, Algebra i Analiz, 15:4 (2003), 61–71; St. Petersburg Math. J., 15:4 (2004), 507–513
Citation in format AMSBIB
\Bibitem{Bir03}
\by M.~Sh.~Birman
\paper Average procedure for periodic operators near an edge of internal gap
\jour Algebra i Analiz
\yr 2003
\vol 15
\issue 4
\pages 61--71
\mathnet{http://mi.mathnet.ru/aa800}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2068979}
\zmath{https://zbmath.org/?q=an:1080.35051}
\transl
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 4
\pages 507--513
\crossref{https://doi.org/10.1090/S1061-0022-04-00819-2}
Linking options:
  • https://www.mathnet.ru/eng/aa800
  • https://www.mathnet.ru/eng/aa/v15/i4/p61
  • This publication is cited in the following 41 articles:
    1. 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
    2. M. A. Dorodnyi, “High-frequency homogenization of multidimensional hyperbolic equations”, Applicable Analysis, 2024, 1  crossref
    3. 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
    4. Richard Craster, Sébastien Guenneau, Muamer Kadic, Martin Wegener, “Mechanical metamaterials”, Rep. Prog. Phys., 86:9 (2023), 094501  crossref
    5. D. I. Borisov, A. I. Mukhametrakhimova, “Uniform convergence for problems with perforation alogn a given manifold and with a nonlinear Robin condition on the boundaries of cavities”, St. Petersburg Math. J., 35:4 (2024), 611–652  mathnet  crossref
    6. Akhmatova A.R. Aksenova E.S. Sloushch V.A. Suslina T.A., “Homogenization of the Parabolic Equation With Periodic Coefficients At the Edge of a Spectral Gap”, Complex Var. Elliptic Equ., 67:3 (2022), 523–555  crossref  mathscinet  isi
    7. A. A. Mishulovich, “Usrednenie mnogomernykh parabolicheskikh uravnenii s periodicheskimi koeffitsientami na krayu vnutrennei lakuny”, Matematicheskie voprosy teorii rasprostraneniya voln. 52, Zap. nauchn. sem. POMI, 516, POMI, SPb., 2022, 135–175  mathnet  mathscinet
    8. A. A. Mishulovich, V. A. Slousch, T. A. Suslina, “Usrednenie odnomernogo periodicheskogo ellipticheskogo operatora na krayu spektralnoi lakuny: operatornye otsenki v energeticheskoi norme”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 50, Zap. nauchn. sem. POMI, 519, POMI, SPb., 2022, 114–151  mathnet  mathscinet
    9. D. I. Borisov, A. I. Mukhametrakhimova, “Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition”, Sb. Math., 212:8 (2021), 1068–1121  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    10. Oudghiri-Idrissi O., Guzina B.B., Meng Sh., “On the Spectral Asymptotics of Waves in Periodic Media With Dirichlet Or Neumann Exclusions”, Q. J. Mech. Appl. Math., 74:2 (2021), 173–221  crossref  mathscinet  isi
    11. Ganesh S.S., Tewary V., “Generic Simplicity of Spectral Edges and Applications to Homogenization”, Asymptotic Anal., 116:3-4 (2020), 219–248  crossref  mathscinet  isi
    12. Berkolaiko G., Kha M., “Degenerate Band Edges in Periodic Quantum Graphs”, Lett. Math. Phys., 110:11 (2020), 2965–2982  crossref  mathscinet  isi  scopus
    13. D. I. Borisov, “Elliptic Operators in Multidimensional Cylinders with Frequently Alternating Boundary Conditions Along a Given Curve”, J Math Sci, 244:3 (2020), 378  crossref
    14. Durante T., “Homogenization of Elliptic Operators in a Strip Perforated Along a Curve”, AIP Conference Proceedings, 2116, eds. Simos T., Tsitouras C., Amer Inst Physics, 2019, 170006  crossref  isi
    15. 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
    16. Cherednichenko K.D. Kiselev A.V., “Norm-Resolvent Convergence of One-Dimensional High-Contrast Periodic Problems to a Kronig–Penney Dipole-Type Model”, Commun. Math. Phys., 349:2 (2017), 441–480  crossref  mathscinet  zmath  isi  elib  scopus
    17. Cardone G., “Waveguides With Fast Oscillating Boundary”, Nanosyst.-Phys. Chem. Math., 8:2 (2017), 160–165  crossref  mathscinet  isi
    18. Korotyaev E. Saburova N., “Effective Masses For Laplacians on Periodic Graphs”, J. Math. Anal. Appl., 436:1 (2016), 104–130  crossref  mathscinet  zmath  isi  elib  scopus
    19. Borisov D. Cardone G. Durante T., “Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve”, Proc. R. Soc. Edinb. Sect. A-Math., 146:6 (2016), 1115–1158  crossref  mathscinet  zmath  isi  elib  scopus
    20. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
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    Алгебра и анализ St. Petersburg Mathematical Journal
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