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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:
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English version: Functional Analysis and Its Applications, 2011, 45:1, 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), 
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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:
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