Maximising Neumann eigenvalues on rectangles

Michiel van den Berg; Dorin Bucur; Katie Gittins

doi:10.1112/blms/bdw049

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arXiv · 1512.00224

Maximising Neumann eigenvalues on rectangles

Michiel van den Berg·Dorin Bucur·Katie Gittins

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Abstract

We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in $\mathbb{R}^2$ 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 Hausdorff metric as $k\rightarrow \infty$. Furthermore, we determine the unique maximiser of the $k$'th Neumann eigenvalue on a rectangle with given perimeter.

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BibTeX RIS

Michiel van den Berg, Dorin Bucur, Katie Gittins. 2016-07-29. Maximising Neumann eigenvalues on rectangles. https://doi.org/10.1112/blms%2Fbdw049

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