Optimisation of the lowest Robin eigenvalue in the exterior of a compact set

David Krejcirik; Vladimir Lotoreichik

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arXiv · 1608.04896

Optimisation of the lowest Robin eigenvalue in the exterior of a compact set

David Krejcirik·Vladimir Lotoreichik

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Abstract

We consider the problem of geometric optimisation of the lowest eigenvalue of the Laplacian in the exterior of a compact planar set, subject to attractive Robin boundary conditions. Under either a constraint of fixed perimeter or area, we show that the maximiser within the class of exteriors of convex sets is always the exterior of a disk. We also argue why the results fail without the convexity constraint and in higher dimensions.

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BibTeX RIS

David Krejcirik, Vladimir Lotoreichik. 2016-08-17. Optimisation of the lowest Robin eigenvalue in the exterior of a compact set. https://arxiv.org/abs/1608.04896

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