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Hearing the shape of a general doubly-connected domain inR 3 with mixed boundary conditions

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Abstract

The basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region inR 3 with mixed boundary conditions, from the complete knowledge of the eigenvalues {λ n } ∞ n=1 for the three-dimensional Laplacian, using the asymptotic expansion of the spectral function\(\Theta (t) = \Sigma _{n = 1}^\infty \exp ( - t\lambda _n )\) ast→0.

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Author notes

  1. E. M. E. Zayed

    Present address: Mathematics Department, University of Emirates, Faculty of Science, P.O. Box 15551, Al-Ain, United Arab Emirates

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  1. Mathematics Department, Zagazig University, Faculty of Science, Zagazig, Egypt

    E. M. E. Zayed

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  1. E. M. E. Zayed
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Zayed, E.M.E. Hearing the shape of a general doubly-connected domain inR 3 with mixed boundary conditions. Z. angew. Math. Phys. 42, 547–564 (1991). https://doi.org/10.1007/BF00946176

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  • DOI: https://doi.org/10.1007/BF00946176

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