The "hot spots" conjecture

Krzysztof Burdzy


Original proposers of the open problem: Jeffrrey Rauch, Bernhard Kawohl, Rodrigo Banuelos
The year when the open problem was proposed: 1974
Sponsor of the submission: Wilfrid Kendall - University of Warwick
AMS Subject classification: 35
Status of the problem: Open

The "hot spots conjecture" of Jeffrey Rauch says that the second Neumann eigenfunction for the Laplacian in a Euclidean domain attains its maximum on the boundary. This general version of the conjecture is known to be false. The conjecture is open for convex domains and simply connected planar domains.

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