A counterexample to the "hot spots" conjecture

Krzysztof Burdzy; Wendelin Werner

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A counterexample to the "hot spots" conjecture

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arxiv math/9803030 v2 pith:BKUZ7ZP4 submitted 1998-03-10 math.PR math.AP

A counterexample to the "hot spots" conjecture

Krzysztof Burdzy , Wendelin Werner This is my paper

classification math.PR math.AP

keywords domainconjecturecounterexamplespotsattainsboundaryboundedconditions

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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.

A counterexample to the "hot spots" conjecture

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