Duke Mathematical Journal

The hot spots problem in planar domains with one hole

Krzysztof Burdzy

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There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.

Article information

Duke Math. J., Volume 129, Number 3 (2005), 481-502.

First available in Project Euclid: 19 October 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)


Burdzy, Krzysztof. The hot spots problem in planar domains with one hole. Duke Math. J. 129 (2005), no. 3, 481--502. doi:10.1215/S0012-7094-05-12932-5. https://projecteuclid.org/euclid.dmj/1129729972

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