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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 5, Pages 1105–1127 (Mi smj1907)  
This article is cited in 26 scientific papers (total in 26 papers)

The spectrum of the elasticity problem for a spiked body

S. A. Nazarov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Full-text PDF (409 kB) Citations (26)
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Abstract: We establish the existence of continuous spectrum for the operator of the linear elasticity problem in a three-dimensional domain with a sufficiently sharp spiked singularity of the boundary. We obtain some information about the structure of the spectrum and verify the weighted Korn inequality, which enables us to prove that the spectrum is discrete for insufficiently sharp spikes. We state some open questions.
Keywords: elasticity equations, zero cusp, spike, discrete spectrum, continuous spectrum.
Received: 12.03.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 5, Pages 874–893
DOI: https://doi.org/10.1007/s11202-008-0087-8
Bibliographic databases:
UDC: 517.946
Language: Russian
Citation: S. A. Nazarov, “The spectrum of the elasticity problem for a spiked body”, Sibirsk. Mat. Zh., 49:5 (2008), 1105–1127; Siberian Math. J., 49:5 (2008), 874–893
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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