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Funktsional. Anal. i Prilozhen., 2009, Volume 43, Issue 3, Pages 92–95 (Mi faa2966)  

This article is cited in 9 scientific papers (total in 9 papers)

Brief communications

A Gap in the Essential Spectrum of the Neumann Problem for an Elliptic System in a Periodic Domain

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences

Abstract: We establish the existence of a gap in the essential spectrum of the Neumann problem for an elliptic formally self-adjoint system of second-order differential equations on a quasi-cylinder (a domain with periodically varying cross-section).

Keywords: gap in essential spectrum, Neumann problem for elliptic system, periodic domain, quasi-cylinder

DOI: https://doi.org/10.4213/faa2966

References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2009, 43:3, 239–241

Bibliographic databases:

UDC: 517.923+517.956.227
Received: 29.05.2008

Citation: S. A. Nazarov, “A Gap in the Essential Spectrum of the Neumann Problem for an Elliptic System in a Periodic Domain”, Funktsional. Anal. i Prilozhen., 43:3 (2009), 92–95; Funct. Anal. Appl., 43:3 (2009), 239–241

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/faa/v43/i3/p92

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. S. A. Nazarov, “On the spectrum of the Laplace operator on the infinite Dirichlet ladder”, St. Petersburg Math. J., 23:6 (2012), 1023–1045  mathnet  crossref  mathscinet  isi  elib  elib
    3. S. A. Nazarov, J. Taskinen, “Structure of the spectrum of the periodic family of identical cells connected through apertures of reducing sizes”, J. Math. Sci. (N. Y.), 194:1 (2013), 72–82  mathnet  crossref  mathscinet
    4. D. I. Borisov, K. V. Pankrashin, “Gap Opening and Split Band Edges in Waveguides Coupled by a Periodic System of Small Windows”, Math. Notes, 93:5 (2013), 660–675  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. 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
    6. Borisov D., Pankrashkin K., “Quantum Waveguides with Small Periodic Perturbations: Gaps and Edges of Brillouin Zones”, J. Phys. A-Math. Theor., 46:23 (2013), 235203  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. S. A. Nazarov, “Gap opening around a given point of the spectrum of a cylindrical waveguide by means of gentle periodic perturbation of walls”, J. Math. Sci. (N. Y.), 206:3 (2015), 288–314  mathnet  crossref
    8. Nazarov S.A., Taskinen J., “Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra”, C. R. Mec., 344:3 (2016), 190–194  crossref  isi  elib  scopus
    9. Mamani C.R., Verri A.A., “Influence of Bounded States in the Neumann Laplacian in a Thin Waveguide”, Rocky Mt. J. Math., 48:6 (2018), 1993–2021  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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