arXiv:1209.2779 Abstract | arXiv Analytics

arXiv:1209.2779 [math.AP]Abstract References Reviews Resources

Inverse backscattering for the Schrödinger equation in 2D

Published 2012-09-13Version 1

We study the inverse backscattering problem for the Schr\"odinger 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.

DOI: 10.1088/0266-5611/23/2/010

Categories: math.AP

Keywords: schrödinger equation, diffraction tomography approximation, hilbertian sobolev spaces, main singularities, inverse backscattering problem

Tags: journal article

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