Increasing stability for determining the potential in the Schr\"odinger equation with attenuation from the Dirichlet-to-Neumann map
Analysis of PDEs
2013-09-12 v1
Abstract
We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schr\"odinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when energy level/frequency is growing. These bounds hold under certain a-priori regularity constraints on the unknown coefficient. Proofs use complex and bounded complex geometrical optics solutions.
Keywords
Cite
@article{arxiv.1309.2840,
title = {Increasing stability for determining the potential in the Schr\"odinger equation with attenuation from the Dirichlet-to-Neumann map},
author = {Victor Isakov and Jenn-Nan Wang},
journal= {arXiv preprint arXiv:1309.2840},
year = {2013}
}