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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find






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


Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 1, Pages 93–96 (Mi faa3020)  

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

On the Spectrum of the Robin Problem in a Domain with a Peak

S. A. Nazarova, Ya. Taskinenb

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
b University of Helsinki

Abstract: A formally self-adjoint Robin–Laplace problem in a peak-shaped domain is considered. The associated quadratic form is not semi-bounded, which is proved to lead to a pathological structure of the spectrum of the corresponding operator. Namely, the residual spectrum of the operator itself and the point spectrum of its adjoint cover the whole complex plane. The operator is not self-adjoint, and the (discrete) spectrum of any of its self-adjoint extensions is not semi-bounded.

Keywords: Robin condition, third boundary value problem, peak, cusp, spectrum, asymptotics, self-adjoint extension

DOI: https://doi.org/10.4213/faa3020

Full text: PDF file (193 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2011, 45:1, 77–79

Bibliographic databases:

UDC: 517.923+517.956.227
Received: 19.08.2009

Citation: S. A. Nazarov, Ya. Taskinen, “On the Spectrum of the Robin Problem in a Domain with a Peak”, Funktsional. Anal. i Prilozhen., 45:1 (2011), 93–96; Funct. Anal. Appl., 45:1 (2011), 77–79

Citation in format AMSBIB
\Bibitem{NazTas11}
\by S.~A.~Nazarov, Ya.~Taskinen
\paper On the Spectrum of the Robin Problem in a Domain with a Peak
\jour Funktsional. Anal. i Prilozhen.
\yr 2011
\vol 45
\issue 1
\pages 93--96
\mathnet{http://mi.mathnet.ru/faa3020}
\crossref{https://doi.org/10.4213/faa3020}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2848745}
\zmath{https://zbmath.org/?q=an:1271.35056}
\transl
\jour Funct. Anal. Appl.
\yr 2011
\vol 45
\issue 1
\pages 77--79
\crossref{https://doi.org/10.1007/s10688-011-0010-0}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000288557800010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952796676}


Linking options:
  • http://mi.mathnet.ru/eng/faa3020
  • https://doi.org/10.4213/faa3020
  • http://mi.mathnet.ru/eng/faa/v45/i1/p93

    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. Kamotski I.V. Maz'ya V.G., “On the linear water wave problem in the presence of a critically submerged body”, SIAM J. Math. Anal., 44:6 (2012), 4222–4249  crossref  mathscinet  zmath  isi  elib  scopus
    2. Daners D., “Principal Eigenvalues for Generalised Indefinite Robin Problems”, Potential Anal., 38:4 (2013), 1047–1069  crossref  mathscinet  zmath  isi  elib  scopus
    3. Bruneau V., Popoff N., “On the negative spectrum of the Robin Laplacian in corner domains”, Anal. PDE, 9:5 (2016), 1259–1283  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
    Number of views:
    This page:268
    Full text:112
    References:45
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021