A Counterexample to the "Hot Spots" Conjecture

Krzysztof Burdzy, Wendelin Werner

Type: Article

Publication Date: 1999-01-01

Citations: 100

DOI: https://doi.org/10.2307/121027

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.

Locations

ResearchWorks at the University of Washington (University of Washington) - View - PDF
Annals of Mathematics - View

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Works Cited by This (4)

Action	Title	Year	Authors
+ PDF Chat	Rearrangements and Convexity of Level Sets in PDE	1985	Bernhard Kawohl
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+	Introduction to Partial Differential Equations	1949	Gerald B. Folland
+	Introduction to Partial Differential Equations	1976	Gerald B. Folland