Maximising Neumann eigenvalues on rectangles

arxiv: 1512.00224 · v4 · pith:YTY5KKWRnew · submitted 2015-12-01 · 🧮 math.SP

Maximising Neumann eigenvalues on rectangles

Michiel van den Berg , Dorin Bucur , Katie Gittins This is my paper

classification 🧮 math.SP

keywords neumanneigenvalueeigenvaluesmeasureperimeterrectanglerectanglesconstraint

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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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Maximising Neumann eigenvalues on rectangles

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