On hearing the shape of an arbitrary doubly-connected region in R2
Elsayed M. E. Zayed · ANZIAM Journal · 1990
Abstract The basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region in R2 together with an impedance condition on its inner boundary and another impedance condition on its outer boundary, from the complete knowledge of the eigenvalues for the two-dimensional Laplacian using the asymptotic expansion of the spectral function for small positive t.