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Algebra i Analiz, 2004, Volume 16, Issue 5, Pages 34–58 (Mi aa630)  

This article is cited in 52 scientific papers (total in 52 papers)

Research Papers

On gaps in the spectrum of some divergence elliptic operators with periodic coefficients

V. V. Zhikov

Vladimir State Pedagogical University

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English version:
St. Petersburg Mathematical Journal, 2005, 16:5, 773–790

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Received: 14.01.2004

Citation: V. V. Zhikov, “On gaps in the spectrum of some divergence elliptic operators with periodic coefficients”, Algebra i Analiz, 16:5 (2004), 34–58; St. Petersburg Math. J., 16:5 (2005), 773–790

Citation in format AMSBIB
\Bibitem{Zhi04}
\by V.~V.~Zhikov
\paper On gaps in the spectrum of some divergence elliptic operators with periodic coefficients
\jour Algebra i Analiz
\yr 2004
\vol 16
\issue 5
\pages 34--58
\mathnet{http://mi.mathnet.ru/aa630}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2106666}
\zmath{https://zbmath.org/?q=an:1174.35458}
\transl
\jour St. Petersburg Math. J.
\yr 2005
\vol 16
\issue 5
\pages 773--790
\crossref{https://doi.org/10.1090/S1061-0022-05-00878-2}


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    This publication is cited in the following articles:
    1. Borisov D.I., “Asymptotics of the spectrum of the Schrödinger operator perturbed by a rapidly oscillating periodic potential”, Dokl. Math., 73:1 (2006), 19–22  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. V. V. Zhikov, S. E. Pastukhova, “On the Trotter–Kato Theorem in a Variable Space”, Funct. Anal. Appl., 41:4 (2007), 264–270  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. D. I. Borisov, R. R. Gadyl'shin, “The spectrum of a self-adjoint differential operator with rapidly oscillating coefficients on the axis”, Sb. Math., 198:8 (2007), 1063–1093  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Babych N.O., Kamotski I.V., Smyshlyaev V.P., “Homogenization of spectral problems in bounded domains with doubly high contrasts”, Netw. Heterog. Media, 3:3 (2008), 413–436  crossref  mathscinet  zmath  isi  elib
    5. S. A. Nazarov, “Opening a gap in the essential spectrum of the elasticity problem in a periodic semi-layer”, St. Petersburg Math. J., 21:2 (2010), 281–307  mathnet  crossref  mathscinet  zmath  isi
    6. S. A. Nazarov, “A Gap in the Essential Spectrum of the Neumann Problem for an Elliptic System in a Periodic Domain”, Funct. Anal. Appl., 43:3 (2009), 239–241  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Cardone G., Minutolo V., Nazarov S.A., “Gaps in the essential spectrum of periodic elastic waveguides”, ZAMM Z. Angew. Math. Mech., 89:9 (2009), 729–741  crossref  mathscinet  zmath  isi  elib  scopus
    8. Smyshlyaev V.P., “Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization”, Mechanics of Materials, 41:4 (2009), 434–447  crossref  isi  scopus
    9. S. A. Nazarov, “Gap detection in the spectrum of an elastic periodic waveguide with a free surface”, Comput. Math. Math. Phys., 49:2 (2009), 323–333  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    10. S. A. Nazarov, “An example of multiple gaps in the spectrum of a periodic waveguide”, Sb. Math., 201:4 (2010), 569–594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. Milton G.W., “Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors”, New J. Phys., 12 (2010), 033035, 11 pp.  crossref  zmath  isi  elib  scopus
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    13. S. A. Nazarov, “Opening of a Gap in the Continuous Spectrum of a Periodically Perturbed Waveguide”, Math. Notes, 87:5 (2010), 738–756  mathnet  crossref  crossref  mathscinet  isi  elib
    14. Nazarov S.A., “Gap in a Continuous Spectrum of an Elastic Waveguide with a Partly Clamped Surface”, Jour. of Appl. Mech. and Tech. Phys., 51:1 (2010), 114–124  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. Cardone G., Nazarov S.A., Perugia C., “A gap in the essential spectrum of a cylindrical waveguide with a periodic perturbation of the surface”, Mathematische Nachrichten, 283:9 (2010), 1222–1244  crossref  mathscinet  zmath  isi  elib  scopus
    16. Nazarov S.A., “Gap in the essential spectrum of an elliptic formally self-adjoint system of differential equations”, Differential Equations, 46:5 (2010), 730–741  crossref  mathscinet  zmath  isi  elib  scopus
    17. Chen Yu., Lipton R., “Tunable double negative band structure from non-magnetic coated rods”, New Journal of Physics, 12 (2010), 083010  crossref  adsnasa  isi  scopus
    18. Cardone G., Durante T., Nazarov S.A., “Localization Effect for Eigenfunctions of the Mixed Boundary Value Problem in a Thin Cylinder with Distorted Ends”, SIAM J Math Anal, 42:6 (2010), 2581–2609  crossref  mathscinet  zmath  isi  elib  scopus
    19. Andrianov I.V., Awrejcewicz J., Danishevs'kyy V.V., Weichert D., “Wave Propagation in Periodic Composites: Higher-Order Asymptotic Analysis Versus Plane-Wave Expansions Method”, Journal of Computational and Nonlinear Dynamics, 6:1 (2011), 011015  crossref  mathscinet  isi  scopus
    20. Fortes S.P., Lipton R.P., Shipman S.P., “Convergent Power Series for Fields in Positive or Negative High-Contrast Periodic Media”, Comm Partial Differential Equations, 36:6 (2011), 1016–1043  crossref  mathscinet  zmath  isi  scopus
    21. Khrabustovskyi A., “Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace–Beltrami operator”, J Differential Equations, 252:3 (2012), 2339–2369  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    22. Piat V.Ch., Nazarov S.A., Ruotsalainen K., “Spectral Gaps for Water Waves Above a Corrugated Bottom”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 469:2149 (2013), 20120545  crossref  mathscinet  zmath  isi  elib  scopus
    23. Bakharev F.L., Nazarov S.A., Ruotsalainen K.M., “A Gap in the Spectrum of the Neumann-Laplacian on a Periodic Waveguide”, Appl. Anal., 92:9 (2013), 1889–1915  crossref  mathscinet  zmath  isi  elib  scopus
    24. Chen Yu., Lipton R., “Resonance and Double Negative Behavior in Metamaterials”, Arch. Ration. Mech. Anal., 209:3 (2013), 835–868  crossref  mathscinet  zmath  isi  elib  scopus
    25. Khrabustovskyi A., “Periodic Elliptic Operators with Asymptotically Preassigned Spectrum”, Asymptotic Anal., 82:1-2 (2013), 1–37  crossref  mathscinet  zmath  isi  elib  scopus
    26. Holovatyi Yu.D., Hut V.M., “Vibrating Systems with Rigid Light-Weight Inclusions: Asymptotics of the Spectrum and Eigenspaces”, Ukr. Math. J., 64:10 (2013), 1495–1513  crossref  mathscinet  zmath  isi  elib  scopus
    27. Chen Yu., Lipton R., “Double Negative Dispersion Relations From Coated Plasmonic Rods”, Multiscale Model. Simul., 11:1 (2013), 192–212  crossref  mathscinet  zmath  isi  elib  scopus
    28. V. V. Zhikov, G. A. Yosifian, “Introduction to the theory of two-scale convergence”, J. Math. Sci. (N. Y.), 197:3 (2014), 325–357  mathnet  crossref  elib
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    30. Bacigalupo A., “Second-Order Homogenization of Periodic Materials Based on Asymptotic Approximation of the Strain Energy: Formulation and Validity Limits”, Meccanica, 49:6 (2014), 1407–1425  crossref  mathscinet  zmath  isi  elib  scopus
    31. Khrabustovskyi A., Khruslov E., “Gaps in the Spectrum of the Neumann Laplacian Generated By a System of Periodically Distributed Traps”, Math. Meth. Appl. Sci., 38:1 (2015), 11–26  crossref  mathscinet  zmath  isi  elib  scopus
    32. Cherednichenko K., Cooper Sh., “Homogenization of the System of High-Contrast Maxwell Equations”, Mathematika, 61:2 (2015), 475–500  crossref  mathscinet  zmath  isi  elib  scopus
    33. Cherednichenko K.D., Cooper S., Guenneau S., “Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems With Periodic Coefficients”, Multiscale Model. Simul., 13:1 (2015), 72–98  crossref  mathscinet  isi  scopus
    34. Cherednichenko K.D. Cooper S., “Resolvent Estimates For High-Contrast Elliptic Problems With Periodic Coefficients”, Arch. Ration. Mech. Anal., 219:3 (2016), 1061–1086  crossref  mathscinet  zmath  isi  elib  scopus
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    38. 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
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    40. Lipton R., Viator Jr. Robert, “Bloch Waves in Crystals and Periodic High Contrast Media”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 51:3 (2017), 889–918  crossref  mathscinet  zmath  isi  scopus
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