Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces

Abstract

We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across $\Sigma \subseteq \Gamma =\partial \Omega$, where $\Omega$ is a bounded open subset of ${\mathbb{R}}^3$ with a Lipschitz boundary. This follows from a uniqueness result in inverse scattering for Schrödinger operators with singular $\delta$-type potential supported on the surface $\Gamma$ and of strength $\alpha \in L^p(\Gamma )$, $p>2$.

Final version, to appear in Journal of Differential Equations

References in corpus (1)

• Schrödinger operators with delta and delta'-potentials supported on hypersurfaces

Cited by in corpus (4)

• Asymptotic Completeness and S-Matrix for Singular Perturbations
• Scattering with critically-singular and $\delta$-shell potentials
• Inverse Scattering for the Laplace operator with boundary conditions on Lipschitz surfaces
• Scattering theory with both regular and singular perturbations