A counterexample to the “hot spots” conjecture

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.

DOI

https://doi.org/10.2307/121027

Authors

Krzysztof Burdy

Wendelin Werner