Loading [MathJax]/jax/output/SVG/config.js
Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find






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


Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 1, Pages 56–70 (Mi timm1142)  

This article is cited in 1 scientific paper (total in 1 paper)

On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case

R. R. Gadyl'shina, S. V. Repjevskijb, E. A. Shishkinaa

a Bashkir State Pedagogical University, Ufa
b Chelyabinsk State University
Full-text PDF (221 kB) Citations (1)
References:
Abstract: A boundary-value problem of finding eigenvalues is considered for the negative Laplace operator in a disk with Neumann boundary condition on almost all circle except for a small arc of vanishing length, where the Dirichlet boundary condition is imposed. Complete asymptotic expansions with respect to a parameter (the length of the small arc) are constructed for an eigenvalue of this problem; the eigenvalue converges to a double eigenvalue of the Neumann problem.
Keywords: Laplace operator; singular perturbation; small parameter; eigenvalue; asymptotics.
Received: 10.12.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 292, Issue 1, Pages 76–90
DOI: https://doi.org/10.1134/S0081543816020073
Bibliographic databases:
Document Type: Article
UDC: 517.928:517.984
Language: Russian
Citation: R. R. Gadyl'shin, S. V. Repjevskij, E. A. Shishkina, “On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 56–70; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 76–90
Citation in format AMSBIB
\Bibitem{GadRepShi15}
\by R.~R.~Gadyl'shin, S.~V.~Repjevskij, E.~A.~Shishkina
\paper On an eigenvalue for the Laplace operator in a disk with Dirichlet boundary condition on a small part of the boundary in a critical case
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 1
\pages 56--70
\mathnet{http://mi.mathnet.ru/timm1142}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379603}
\elib{https://elibrary.ru/item.asp?id=23137971}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2016
\vol 292
\issue , suppl. 1
\pages 76--90
\crossref{https://doi.org/10.1134/S0081543816020073}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000376272600007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971500276}
Linking options:
  • https://www.mathnet.ru/eng/timm1142
  • https://www.mathnet.ru/eng/timm/v21/i1/p56
  • This publication is cited in the following 1 articles:
    1. R. R. Gadylshin, A. A. Ershov, S. V. Repyevsky, “On asymptotic formula for electric resistance of conductor with small contacts”, Ufa Math. J., 7:3 (2015), 15–27  mathnet  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:414
    Full-text PDF :112
    References:75
    First page:15
     
      Contact us:
    math-net2025_05@mi-ras.ru
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025