Estimates for the Second Order Derivatives of Eigenvectors in Thin Anisotropic Plates with Variable Thickness |
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Authors: | S A Nazarov |
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Institution: | (1) Institute of Applied Engineering, Russian Academy of Sciences, St. Petersburg, Russia |
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Abstract: | For the second order derivatives of eigenvectors in a thin anisotropic heterogeneous plate Ωh, we derive estimates of their weighted L2-norms with majorants whose dependence on the plate thickness h and on the eigenvalue number is expressed explicitly. These
estimates maintain the asymptotic sharpness throughout the entire spectrum, whereas inside its low-frequency band the majorants
remain bounded as h → +0. The latter is a rather unexpected fact, because for the first eigenfunction u1 of a similar boundary-value problem for a scalar second order differential operator with variable coefficients, the norm
‖∇
x
2
u0; L2(Ωh)‖ is of order h−1 and grows as h tends to zero. Bibliography: 35 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 161–180. |
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