Abstract. We consider the direct and inverse obstacle scattering problem for the Laplace–Beltrami operator with complex-valued electromagnetic potentials where outside of some large ball the operator is simply the negative Laplacian. It is assumed there are an arbitrary number of impenetrable obstacles with various boundary conditions (including mixed boundary conditions, i.e., partially coated obstacles). We prove that given the scattering amplitude a(θ, ω, k) for all θ, ω Sⁿ⁻¹ and any fixed k > 0, the location of the obstacles and their respective boundary conditions are uniquely determined. In addition, we give a new proof of the asymptotic expansion of the Green's function in terms of distorted plane waves and, as an immediate corollary, prove the determination of the Dirichlet-to-Neumann operator from the scattering data.

Print publication: Issue 5 (October 2006)
Received 29 April 2006, in final form 10 July 2006
Published 4 August 2006