Robin spectrum: two disks maximize the third eigenvalue

Alexandre Girouard; Richard S. Laugesen

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arXiv · 1907.13173

Robin spectrum: two disks maximize the third eigenvalue

Alexandre Girouard·Richard S. Laugesen

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Abstract

The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the third eigenvalue of a disjoint union of two disks, provided the Robin parameter lies in a certain range and is scaled in each case by the length of the boundary. Equality is achieved when the domain degenerates suitably to the two disks.

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Alexandre Girouard, Richard S. Laugesen. 2019-07-30. Robin spectrum: two disks maximize the third eigenvalue. https://arxiv.org/abs/1907.13173

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