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.
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Dedicated to the Memory of Sergeĭ L’vovich Sobolev.
Original Russian Text Copyright © 2008 Nazarov S. A.
The author was partially supported by the Netherlands Organization for Scientific Research (NWO) and the Russian Foundation for Basic Research (Joint Grant 047.017.020).
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St. Petersburg. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 5, pp. 1105–1127, September–October, 2008.
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Nazarov, S.A. The spectrum of the elasticity problem for a spiked body. Sib Math J 49, 874–893 (2008). https://doi.org/10.1007/s11202-008-0087-8
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DOI: https://doi.org/10.1007/s11202-008-0087-8