The point source inverse back-scattering problem
Analysis of PDEs
2014-03-10 v1
Abstract
We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering problem. We show that if the angular derivatives of the difference of two potentials having the same data is controlled by the L^2 norm of the difference of the potentials they must be equal. In particular this shows injectivity of the inverse problem for radial potentials.
Cite
@article{arxiv.1403.1766,
title = {The point source inverse back-scattering problem},
author = {Rakesh and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1403.1766},
year = {2014}
}