The spectrum of the elasticity problem for a spiked body |
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Authors: | S A Nazarov |
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Institution: | (1) Institute of Problems of Mechanical Engineering, St. Petersburg, Russia |
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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. |
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Keywords: | elasticity equations zero cusp spike discrete spectrum continuous spectrum |
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