Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces

摘要

We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across Sigma subset of Gamma = partial derivative Omega, where Omega is a bounded open subset of R-3 with a Lipschitz boundary. This follows from a uniqueness result in inverse scattering for Schrodinger operators with singular delta-type potential supported on the surface Gamma and of strength alpha is an element of L-p (Gamma), p 2. (C) 2018 Elsevier Inc. All rights reserved.