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  • American Institute of Physics (AIP)  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Hearing the shape of a general doubly connected domain in R3 with impedance boundary conditions (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2361-2365 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The basic problem in this paper is that of determining the geometry of a general doubly connected domain in R3 together with an impedance condition on its inner bounding surface and another impedance condition on its outer bounding surface, from the complete knowledge of the eigenvalues {λj}∞j=1 for the three-dimensional Laplacian using the asymptotic expansion of the spectral function θ(t)=∑∞j=1 exp(−tλj) for small positive t.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528837
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On hearing the shape of rectilinear regions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3490-3496 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: From complete knowledge of the eigenvalues of the negative Laplacian on a bounded domain, one may extract information on the geometry and the boundary conditions by analyzing the asymptotic expansion of a spectral function. Explicit calculations are performed for an equilateral triangular domain with Dirichlet or Neumann boundary conditions, yielding in particular the corner angle terms. In three dimensions, some applications to eigenvalue problems for an equilateral triangular prism are dealt with, including the solid vertex terms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530480
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    Paper (German National Licenses)
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