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Funktsional'nyi Analiz i ego Prilozheniya, 2011, Volume 45, Issue 1, Pages 93–96
DOI: https://doi.org/10.4213/faa3020 (Mi faa3020) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (193 kB) Citations (5)
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DOI: https://doi.org/10.4213/faa3020
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.
Received: 19.08.2009
English version:
Functional Analysis and Its Applications, 2011, Volume 45, Issue 1, Pages 77–79
DOI: https://doi.org/10.1007/s10688-011-0010-0
Bibliographic databases:
Document Type: Article
UDC: 517.923+517.956.227
Language: Russian
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
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  • https://www.mathnet.ru/eng/faa/v45/i1/p93
    • This publication is cited in the following 5 articles:
    1. Nazarov S.A., Popoff N., Taskinen J., “Plummeting and Blinking Eigenvalues of the Robin Laplacian in a Cuspidal Domain”, Proc. R. Soc. Edinb. Sect. A-Math., 150:6 (2020), PII S0308210519000489, 2871–2893  crossref  mathscinet  zmath  isi
    2. 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
    3. Daners D., “Principal Eigenvalues for Generalised Indefinite Robin Problems”, Potential Anal., 38:4 (2013), 1047–1069  crossref  mathscinet  zmath  isi  elib  scopus
    4. T. A. Mel'nik, D. Yu. Sadovyi, “Homogenization of Boundary Value Problems in Two-Level Thick Junctions Consisting of Thin Disks with Rounded or Sharp Edges”, J Math Sci, 191:2 (2013), 254  crossref
    5. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Abstract page:533
    Full-text PDF :232
    References:109
    First page:11
     
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