Maximising Neumann eigenvalues on rectangles

Michiel van den Berg; Katie Gittins; Dorin Bucur

doi:10.1112/blms/bdw049

Maximising Neumann eigenvalues on rectangles

Michiel van den Berg, Katie Gittins, Dorin Bucur

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Abstract

We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in R² with a measure or perimeter constraint. We show that the rectangle with measure 1 which maximises the k'th Neumann eigenvalue converges to the unit square in the Hausdor metric as k → ∞. Furthermore, we determine the unique maximiser of the k'th Neumann eigenvalue on a rectangle with given perimeter.

Original language	English
Pages (from-to)	877-894
Number of pages	18
Journal	Bulletin of the London Mathematical Society
Volume	48
Issue number	5
Early online date	8 Aug 2016
DOIs	https://doi.org/10.1112/blms/bdw049
Publication status	Published - Oct 2016

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10.1112/blms/bdw049

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Oxford University Press at http://blms.oxfordjournals.org/content/early/2016/08/08/blms.bdw049.short. Please refer to any applicable terms of use of the publisher.
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Emeritus Professor Michiel van den Berg
- M.vandenBergbristol.acuk
- School of Mathematics - Emeritus Professor
- Probability, Analysis and Dynamics
- Pure Mathematics
- Analysis
Person: Member, Honorary and Visiting Academic

Cite this

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AB - We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in R2 with a measure or perimeter constraint. We show that the rectangle with measure 1 which maximises the k'th Neumann eigenvalue converges to the unit square in the Hausdor metric as k → ∞. Furthermore, we determine the unique maximiser of the k'th Neumann eigenvalue on a rectangle with given perimeter.

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M3 - Article (Academic Journal)

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Maximising Neumann eigenvalues on rectangles

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Emeritus Professor Michiel van den Berg

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