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Licensed 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 EMAIL logo
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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

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