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Matematicheskie Zametki, 2005, Volume 78, Issue 2, Pages 299–307
DOI: https://doi.org/10.4213/mzm2575 (Mi mzm2575) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary

M. I. Cherdantsev

Ufa State Aviation Technical University
Full-text PDF (192 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm2575
Abstract: In this paper, we consider eigenvalue problems for the Laplace operator in three-dimensional domains with singularly perturbed boundary. Perturbations are generated by a complementary Dirichlet boundary condition on a small nonclosed surface inside the domain. The convergence and the asymptotic behavior of simple eigenvalues of the problem are considered.
Received: 24.08.2004
Revised: 27.12.2004
English version:
Mathematical Notes, 2005, Volume 78, Issue 2, Pages 270–278
DOI: https://doi.org/10.1007/s11006-005-0125-9
Bibliographic databases:
UDC: 571.958
Language: Russian
Citation: M. I. Cherdantsev, “Asymptotic Expansion of Eigenvalues of the Laplace Operator in Domains with Singularly Perturbed Boundary”, Mat. Zametki, 78:2 (2005), 299–307; Math. Notes, 78:2 (2005), 270–278
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. Medet Nursultanov, William Trad, Justin Tzou, Leo Tzou, “Eigenvalue variations of the Neumann Laplace operator due to perturbed boundary conditions”, Res Math Sci, 12:1 (2025)  crossref
    2. N. N. Abdullazade, G. A. Chechkin, “Perturbation of the Steklov Problem on a Small Part of the Boundary”, J Math Sci, 196:4 (2014), 441  crossref
    3. Chechkin G.A., Koroleva Yu.O., Meidell A., Persson L.-E., “On the Friedrichs inequality in a domain perforated aperiodically along the boundary. Homogenization procedure. Asymptotics for parabolic problems”, Russ. J. Math. Phys., 16:1 (2009), 1–16  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. A. G. Chechkina, “Convergence of solutions and eigenelements of Steklov type boundary value problems with boundary conditions of rapidly varying type”, J Math Sci, 162:3 (2009), 443  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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