RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2013, Volume 174, Number 3, Pages 398–415 (Mi tmf8376)  

This article is cited in 6 scientific papers (total in 6 papers)

Spectral properties of a thin layer with a doubly periodic family of thinning regions

S. A. Nazarov

St. Petersburg State University, St. Petersburg, Russia

Abstract: We show that the spectrum of the Dirichlet problem for the Laplace operator in a layer with a doubly periodic structure has gaps and determine several characteristics of their location. The result is obtained by asymptotic analysis of a model spectral problem on the periodicity cell.

Keywords: Dirichlet problem in a doubly periodic layer, asymptotic behavior, eigenvalue localization, spectral gap

DOI: https://doi.org/10.4213/tmf8376

Full text: PDF file (545 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2013, 174:3, 343–359

Bibliographic databases:

Received: 04.06.2012

Citation: S. A. Nazarov, “Spectral properties of a thin layer with a doubly periodic family of thinning regions”, TMF, 174:3 (2013), 398–415; Theoret. and Math. Phys., 174:3 (2013), 343–359

Citation in format AMSBIB
\Bibitem{Naz13}
\by S.~A.~Nazarov
\paper Spectral properties of a~thin layer with a~doubly periodic family of thinning regions
\jour TMF
\yr 2013
\vol 174
\issue 3
\pages 398--415
\mathnet{http://mi.mathnet.ru/tmf8376}
\crossref{https://doi.org/10.4213/tmf8376}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3171515}
\zmath{https://zbmath.org/?q=an:1287.35052}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2013TMP...174..343N}
\elib{http://elibrary.ru/item.asp?id=20732590}
\transl
\jour Theoret. and Math. Phys.
\yr 2013
\vol 174
\issue 3
\pages 343--359
\crossref{https://doi.org/10.1007/s11232-013-0031-3}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000317346700004}
\elib{http://elibrary.ru/item.asp?id=20430962}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84875997614}


Linking options:
  • http://mi.mathnet.ru/eng/tmf8376
  • https://doi.org/10.4213/tmf8376
  • http://mi.mathnet.ru/eng/tmf/v174/i3/p398

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Asymptotics of eigenvalues of the Dirichlet problem in a skewed $\mathcal{T}$-shaped waveguide”, Comput. Math. Math. Phys., 54:5 (2014), 793–814  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. S. A. Nazarov, “Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube”, Trans. Moscow Math. Soc., 76:1 (2015), 1–53  mathnet  crossref  elib
    3. S. A. Nazarov, “Eigenmodes of a thin elastic layer between periodic rigid profiles”, Comput. Math. Math. Phys., 55:10 (2015), 1684–1697  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Nazarov S.A., “Asymptotics of the natural oscillations of a thin elastic gasket between absolutely rigid profiles”, Pmm-J. Appl. Math. Mech., 79:6 (2015), 577–586  crossref  mathscinet  isi  scopus
    5. S. A. Nazarov, “Discrete spectrum of cranked quantum and elastic waveguides”, Comput. Math. Math. Phys., 56:5 (2016), 864–880  mathnet  crossref  crossref  isi  elib
    6. Nazarov S.A., Perez E., Taskinen J., “Localization effect for Dirichlet eigenfunctions in thin non-smooth domains”, Trans. Am. Math. Soc., 368:7 (2016), 4787–4829  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:274
    Full text:51
    References:43
    First page:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019