Exponential instability in the Gel'fand inverse problem on the energy intervals

Details Exponential instability in the Gel'fand inverse problem on the energy intervals Exponential instability in the Gel'fand inverse problem on the energy intervals

2010-12-10

arxiv.org/abs/1012.2193v1

Journal of Inverse and Ill-posed Problems 19, 3 (2011) 453-473

Mathematics

Analysis of PDEs

Scientific paper

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).

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