Inverse backscattering for the Schr\"odinger equation in 2D
Analysis of PDEs
2012-09-14 v1
Abstract
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.
Cite
@article{arxiv.1209.2779,
title = {Inverse backscattering for the Schr\"odinger equation in 2D},
author = {Juan Manuel Reyes},
journal= {arXiv preprint arXiv:1209.2779},
year = {2012}
}