A counterexample to the "hot spots" conjecture

Details A counterexample to the "hot spots" conjecture A counterexample to the "hot spots" conjecture

1998-03-10

arxiv.org/abs/math/9803030v2

Ann. of Math. (2) 149 (1999), no. 1, 309-317

Mathematics

Probability

9 pages, published version

Scientific paper

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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