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arXiv · 1604.01601

Inverse obstacle scattering with non-over-determined data

A. G. Ramm
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Abstract

It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the obstacle $D$ and the boundary condition on $S$. The boundary condition on $S$ is assumed to be the Dirichlet, or Neumann, or the impedance one. The uniqueness theorem for the solution of multidimensional inverse scattering problems with non-over-determined data was not known for many decades. Such a theorem is proved in this paper for inverse scattering by obstacles for the first time.

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A. G. Ramm. 2016-04-06. Inverse obstacle scattering with non-over-determined data. https://arxiv.org/abs/1604.01601

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