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arXiv · 1702.05312

Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces

Andrea Mantile·Andrea Posilicano·Mourad Sini
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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 Schr\"odinger operators with singular $\delta$-type potential supported on the surface $\Gamma$ and of strength $\alpha\in L^{p}(\Gamma)$, $p>2$.

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Andrea Mantile, Andrea Posilicano, Mourad Sini. 2017-02-17. Uniqueness in inverse acoustic scattering with unbounded gradient across Lipschitz surfaces. https://doi.org/10.1016/j.jde.2018.05.029

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