Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
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

Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 195, Number 2, Pages 225–239
DOI: https://doi.org/10.4213/tmf9411 (Mi tmf9411) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip

D.I. Borisovabc

a Institute of Mathematics with Computing Centre, Ufa Science Center, RAS, Ufa, Russia
b Akhmulla Bashkir State Pedagogical University, Ufa, Russia
c University of Hradec Králové, Hradec Králové, Czech Republic
Full-text PDF (441 kB) Citations (5)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf9411
Abstract: We consider the Laplacian in a planar infinite straight strip with frequent alternation of boundary conditions. We show that for a sufficiently small alternation period, there are no gaps in a lower part of the spectrum. In terms of certain numbers and functions, we write an explicit upper bound for the period and an expression for the length of the lower part of the spectrum in which the absence of gaps is guaranteed.
Keywords: Bethe–Sommerfeld conjecture, gap, periodic operator, alternation of boundary conditions, Laplacian, infinite strip.
Funding agency Grant number
Russian Science Foundation 17-11-01004
This research was supported by a grant from the Russian Science Foundation (Project No. 17-11-01004).
Received: 03.06.2017
Revised: 07.08.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 195, Issue 2, Pages 690–703
DOI: https://doi.org/10.1134/S0040577918050057
Bibliographic databases:
Document Type: Article
MSC: 35B27, 35P05
Language: Russian
Citation: D.I. Borisov, “Absence of gaps in a lower part of the spectrum of a Laplacian with frequent alternation of boundary conditions in a strip”, TMF, 195:2 (2018), 225–239; Theoret. and Math. Phys., 195:2 (2018), 690–703
Citation in format AMSBIB
\Bibitem{Bor18}
\by D.I.~Borisov
\paper Absence of gaps in a~lower part of the~spectrum of a~Laplacian with frequent alternation of boundary conditions in a~strip
\jour TMF
\yr 2018
\vol 195
\issue 2
\pages 225--239
\mathnet{http://mi.mathnet.ru/tmf9411}
\crossref{https://doi.org/10.4213/tmf9411}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3795160}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...195..690B}
\elib{https://elibrary.ru/item.asp?id=32823071}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 195
\issue 2
\pages 690--703
\crossref{https://doi.org/10.1134/S0040577918050057}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000434491300005}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85048252508}
Linking options:
  • https://www.mathnet.ru/eng/tmf9411
  • https://doi.org/10.4213/tmf9411
  • https://www.mathnet.ru/eng/tmf/v195/i2/p225
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:357
    Full-text PDF :74
    References:40
    First page:15
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024