Minimising Dirichlet eigenvalues on cuboids of unit measure

Michiel van den Berg; Katie Gittins

doi:10.1112/S0025579316000413

Minimising Dirichlet eigenvalues on cuboids of unit measure

Michiel van den Berg, Katie Gittins

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Abstract

We consider the minimization of Dirichlet eigenvalues λk휆k , k∈Nk∈N , of the Laplacian on cuboids of unit measure in R3R3 . We prove that any sequence of optimal cuboids in R3R3 converges to a cube of unit measure in the sense of Hausdorff as k→∞k→∞ . We also obtain an upper bound for that rate of convergence.

Original language	English
Pages (from-to)	469-482
Number of pages	14
Journal	Mathematika
Volume	63
Issue number	2
Early online date	13 Mar 2017
DOIs	https://doi.org/10.1112/S0025579316000413
Publication status	Published - 2017

Keywords

Spectral optimisation
Dirichlet eigenvalues

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via CUP at https://www.cambridge.org/core/journals/mathematika/article/minimizing-dirichlet-eigenvalues-on-cuboids-of-unit-measure/0DA0B370CA5866549CD628A8725DE0B6 . Please refer to any applicable terms of use of the publisher.
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title = "Minimising Dirichlet eigenvalues on cuboids of unit measure",

abstract = "We consider the minimization of Dirichlet eigenvalues λk휆k , k∈Nk∈N , of the Laplacian on cuboids of unit measure in R3R3 . We prove that any sequence of optimal cuboids in R3R3 converges to a cube of unit measure in the sense of Hausdorff as k→∞k→∞ . We also obtain an upper bound for that rate of convergence.",

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T1 - Minimising Dirichlet eigenvalues on cuboids of unit measure

AU - van den Berg, Michiel

AU - Gittins, Katie

PY - 2017

Y1 - 2017

N2 - We consider the minimization of Dirichlet eigenvalues λk휆k , k∈Nk∈N , of the Laplacian on cuboids of unit measure in R3R3 . We prove that any sequence of optimal cuboids in R3R3 converges to a cube of unit measure in the sense of Hausdorff as k→∞k→∞ . We also obtain an upper bound for that rate of convergence.

AB - We consider the minimization of Dirichlet eigenvalues λk휆k , k∈Nk∈N , of the Laplacian on cuboids of unit measure in R3R3 . We prove that any sequence of optimal cuboids in R3R3 converges to a cube of unit measure in the sense of Hausdorff as k→∞k→∞ . We also obtain an upper bound for that rate of convergence.

KW - Spectral optimisation

KW - Dirichlet eigenvalues

UR - https://arxiv.org/abs/1607.02087

U2 - 10.1112/S0025579316000413

DO - 10.1112/S0025579316000413

M3 - Article (Academic Journal)

SN - 0025-5793

VL - 63

SP - 469

EP - 482

JO - Mathematika

JF - Mathematika

IS - 2

ER -

Minimising Dirichlet eigenvalues on cuboids of unit measure

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Keywords

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