Maximising Neumann eigenvalues on rectangles

Michiel van den Berg, Katie Gittins, Dorin Bucur

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

17 Citations (Scopus)
274 Downloads (Pure)


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 languageEnglish
Pages (from-to)877-894
Number of pages18
JournalBulletin of the London Mathematical Society
Issue number5
Early online date8 Aug 2016
Publication statusPublished - Oct 2016


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