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The buckling eigenvalue problem in the annulus

École Polytechnique Fédérale de Lausanne, MATH SCI-SB-JS, Station 8, CH-1015 Lausanne, Switzerland

Corresponding author.

and

Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 39 Rue Frederic Joliot Curie, 13453 Marseille CEDEX 13, France

E-mail Address: enea.parini@univ-amu.fr

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https://doi.org/10.1142/S0219199720500443Cited by:3 (Source: Crossref)

Abstract

We consider the buckling eigenvalue problem for a clamped plate in the annulus. We identify the first eigenvalue in dependence of the inner radius, and study the number of nodal domains of the corresponding eigenfunctions. Moreover, in order to investigate the asymptotic behavior of eigenvalues and eigenfunctions as the inner radius approaches the outer one, we provide an analytical study of the buckling problem in rectangles with mixed boundary conditions.

Keywords:

AMSC: 35P15, 35B09, 35J30, 74K20

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