Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles

D. Buoso; P. Freitas

doi:10.1090/proc/14792

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles

D. Buoso, P. Freitas

Research output: Contribution to journal › Article › peer-review

Abstract

We study the behaviour of extremal eigenvalues of the Dirichlet biharmonic operator over rectangles with a given fixed area. We begin by proving that the principal eigenvalue is minimal for a rectangle for which the ratio between the longest and the shortest side lengths does not exceed 1.066459. We then consider the sequence formed by the minimal kth eigenvalue and show that the corresponding sequence of minimising rectangles converges to the square as k goes to infinity.

Original language	English
Pages (from-to)	1109-1120
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	3
DOIs	https://doi.org/10.1090/proc/14792
Publication status	Published - 2020
Externally published	Yes

Keywords

Biharmonic operator
Eigenvalues
Isoperimetric inequality
Rectangles
Shape optimisation

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10.1090/proc/14792

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KW - Biharmonic operator

KW - Eigenvalues

KW - Isoperimetric inequality

KW - Rectangles

KW - Shape optimisation

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Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles

Abstract

Keywords

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