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The "hot spots" problem in planar domains with one hole

Krzysztof Burdzy
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Abstract

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.

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Krzysztof Burdzy. 2004-05-25. The "hot spots" problem in planar domains with one hole. https://arxiv.org/abs/math/0405472

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