Duke Mathematical Journal

The hot spots problem in planar domains with one hole

Krzysztof Burdzy

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Abstract

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

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

Dates
First available in Project Euclid: 19 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1129729972

Digital Object Identifier
doi:10.1215/S0012-7094-05-12932-5

Mathematical Reviews number (MathSciNet)
MR2169871

Zentralblatt MATH identifier
1154.35330

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

Citation

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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References

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