Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
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Source Normalized Impact per Paper (SNIP) 2016: 1.125
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Exponential instability in the Gel'fand inverse problem on the energy intervals
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).
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