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Accessible Unlicensed Requires Authentication Published by De Gruyter August 5, 2011

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

Mikhail Ismailovitch Isaev
From the journal


We consider the Gel'fand inverse problem and continue studies of Mandache (Inverse Problems 17: 1435–1444, 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 (Appl. Anal. 27: 153–172, 1988), Novikov and Santacesaria (J. Inverse Ill-Posed Probl., 2010) and especially of Novikov (2010) are optimal (up to the value of the exponent).

Received: 2011-01-03
Published Online: 2011-08-05
Published in Print: 2011-August

© de Gruyter 2011