We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across Σ⊆Γ=∂Ω where Ω is a bounded open subset of R3with a Lipschitz boundary. This follows from a uniqueness result in inverse scattering for Schrödinger operators with singular δ-type potential supported on the surface Γ and of strength α∈Lp(Γ), p>2.
Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces
Posilicano, Andrea;
2018-01-01
Abstract
We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across Σ⊆Γ=∂Ω where Ω is a bounded open subset of R3with a Lipschitz boundary. This follows from a uniqueness result in inverse scattering for Schrödinger operators with singular δ-type potential supported on the surface Γ and of strength α∈Lp(Γ), p>2.
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