Comptes Rendus
Asymptotically sharp uniform estimates in a scalar spectral stiff problem
Comptes Rendus. Mécanique, Volume 331 (2003) no. 5, pp. 325-330.

Estimates of convergence rates for rescaled eigenvalues of the stiff Neumann problem for the Laplacian are obtained. The bounds are expressed in terms of the stiffness ratio and properties of the limit spectrum both for low and middle frequency ranges.

On obtienent des estimations de la vitesse de convergence des valeurs propres, convenablement mises a l'échelle, d'un problème de Neumann raide pour l'operateur de Laplace. Des bornes correspondantes a ces estimations sont exprimées en termes du rapport des raideurs et des propriétés du spectre limite dans les rangs des fréquences basses et moyennes.

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Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00073-1
Keywords: Acoustics, Waves, Vibrations, Stiff problem, Spectral analysis, Low frequencies, Middle frequencies
Mot clés : Acoustique, Ondes, Vibrations, Problème raide, Analyse spectrale, Basses fréquences, Moyennes fréquences

Miguel Lobo 1; Serguei A. Nazarov 2; Eugenia Pérez 3

1 Departamento de Matemáticas, Estadı́stica y Computación, Universidad de Cantabria, Av. de los Castros, s/n. 39005 Santander, Spain
2 Institute of Mechanical Engineering Problems, RAN V. O. Bol'shoi pr., 61, 199178 St Petersburg, Russia
3 Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Av. de los Castros, s/n. 39005 Santander, Spain
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Miguel Lobo; Serguei A. Nazarov; Eugenia Pérez. Asymptotically sharp uniform estimates in a scalar spectral stiff problem. Comptes Rendus. Mécanique, Volume 331 (2003) no. 5, pp. 325-330. doi : 10.1016/S1631-0721(03)00073-1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00073-1/

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[5] M. Lobo, S.A. Nazarov, E. Pérez, Eigenoscillations of contrastly non-homogeneous elastic body. Asymptotic and uniform estimates for the eigenvalues, in preparation

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[9] S.A. Nazarov Estimating the convergence rate for eigenfrequences of anisotropic plates with variable thickness, C. R. Mecanique, Volume 330 (2002), pp. 603-607

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