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arXiv · 1209.2779

Inverse backscattering for the Schrödinger equation in 2D

Juan Manuel Reyes
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Abstract

We study the inverse backscattering problem for the Schrödinger equation in two dimensions. We prove that, for a non-smooth potential in 2D the main singularities up to 1/2 of the derivative of the potential are contained in the Born approximation (Diffraction Tomography approximation) constructed from the backscattering data. We measure singularities in the scale of Hilbertian Sobolev spaces.

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Juan Manuel Reyes. 2012-09-13. Inverse backscattering for the Schrödinger equation in 2D. https://doi.org/10.1088/0266-5611%2F23%2F2%2F010

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