EMIS ELibM Electronic Journals Annals of Mathematics, II. Series
Vol. 149, No. 1, pp. 309-317 (1999)

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A counterexample to the ``hot spots'' conjecture

Krzysztof Burdzy and Wendelin Werner

Abstract: We construct a counterexample to the ``hot spots'' conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point of that domain.

Keywords: second eigenvalue of the Laplacian

Classification (MSC2000): 35P15 35J05 35B05

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Electronic fulltext finalized on: 18 Aug 2001. This page was last modified: 21 Jan 2002.

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