Hearing the shape of a general doubly connected domain in R3 with impedance boundary conditions
Elsayed M. E. Zayed · Journal of Mathematical Physics · 1990
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.