Reconstruction and stability for piecewise smooth potentials in the plane
Analysis of PDEs
2016-07-18 v2
Abstract
We show that potentials with jump discontinuities can be recovered from the Dirichlet-to-Neumann map using Bukhgeim's method. Combining with known formulas, this enables the recovery from the scattering amplitude at a fixed energy. We also provide a priori stability estimates for reconstruction from the Dirichlet-to-Neumann map as well as from the scattering amplitudegiven an approximate knowledge of the location of the discontinuities.
Cite
@article{arxiv.1606.03020,
title = {Reconstruction and stability for piecewise smooth potentials in the plane},
author = {Jorge Tejero},
journal= {arXiv preprint arXiv:1606.03020},
year = {2016}
}