Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

Arrieta, José M.; Ferraresso, Francesco; Lamberti, Pier Domenico (2017). Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains. Integral equations and operator theory, 89(3), pp. 377-408. Birkhäuser 10.1007/s00020-017-2391-9

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We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Ferraresso, Francesco

Subjects:

500 Science > 510 Mathematics

ISSN:

0378-620X

Publisher:

Birkhäuser

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

19 Sep 2019 08:42

Last Modified:

23 Oct 2019 08:01

Publisher DOI:

10.1007/s00020-017-2391-9

BORIS DOI:

10.7892/boris.125532

URI:

https://boris.unibe.ch/id/eprint/125532

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