Exponential instability in the Gel'fand inverse problem on the energy intervals
Analysis of PDEs
2011-12-16 v1
Abstract
We consider the Gel'fand inverse problem and continue studies of [Mandache,2001]. We show that the Mandache-type instability remains valid even in the case of Dirichlet-to-Neumann map given on the energy intervals. These instability results show, in particular, that the logarithmic stability estimates of [Alessandrini,1988], [Novikov,Santacesaria,2010] and especially of [Novikov,2010] are optimal (up to the value of the exponent).
Cite
@article{arxiv.1012.2193,
title = {Exponential instability in the Gel'fand inverse problem on the energy intervals},
author = {Mikhail Isaev},
journal= {arXiv preprint arXiv:1012.2193},
year = {2011}
}