HEARING THE SHAPE OF A GENERAL DOUBLY-CONNECTED DOMAIN IN R3 WITH MIXED BOUNDARY-CONDITIONS

The basic problem in this paper is that of determining the geometry of an arbitrary doubly-connected region in R3 with mixed boundary conditions, from the complete knowledge of the eigenvalues \{lambda-n\}n = 1 infinity for the three-dimensional Laplacian, using the asymptotic expansion of the spectral function THETA-(t) = SIGMA-n = 1 infinity exp(-t-lambda-n) as t -> 0.