A counterexample to the "hot spots" conjecture

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Date

1999-01

Authors

Burdzy, Krzysztof
Werner, Wendelin

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Publisher

Princeton University and Institute for Advanced Study

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.

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Keywords

eigenvalues, Hot spots, Laplacian, Neumann boundary conditions, eigenfunction

Citation

Burdzy, K. & W. Werner. (1999). A counterexample to the "hot spots" conjecture. Annals of Mathematics, 149(1), 309-317.

URI

http://hdl.handle.net/1773/2198

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EPrint Collection - Mathematics