Scattering theory for bulk and surface waves in an impedance half-space, II: local perturbations, the scattering matrix and an inverse problem

We study the Robin, or impedance, Laplacian on a half-space of dimension $n \ge 3$ which is perturbed inside a fixed ball. The boundary may be deformed, and obstacles may be present in the interior or attached to the boundary, in any combination and with no smallness assumption. Outside the ball the