Minimising Dirichlet eigenvalues on cuboids of unit measure

Michiel van den Berg, Katie Gittins

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)
258 Downloads (Pure)


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 languageEnglish
Pages (from-to)469-482
Number of pages14
Issue number2
Early online date13 Mar 2017
Publication statusPublished - 2017


  • Spectral optimisation
  • Dirichlet eigenvalues

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