We prove uniqueness in inverse acoustic scattering in the case
the density of the medium has an unbounded gradient across Σ⊆∂Ω, where Ω
is a 3D-Lipschitz domain. The corresponding direct problem is related to
the stationary waves scattering for 3D Schrödinger operators with δ-type
singular perturbations supported on ∂Ω and of strength α∈L^p(∂Ω), p>2.
This is a multiple scattering problem from obstacles and potentials
whose solutions depend on the obstacles locations and shapes, the
related transmission impedances and the background potentials. The
inverse problem then consists in determining these scattering parameters
from a complete set of far-field data at a fixed energy. In this
framework, we show that the acoustic far-field pattern can be defined in
terms of the scattering amplitude for the corresponding Schrödinger
operator. A uniqueness result is then obtained by using new estimates
for complex geometrical optics solutions (recently provided by B.
Haberman for the Calderon’s problem).