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

Mikhail Isaev (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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).

Domaines: Equations aux dérivées partielles [math.AP]

Mikhail Isaev. Exponential instability in the Gel'fand inverse problem on the energy intervals. Journal of Inverse and Ill-posed Problems, 2011, 19 (3), pp.453-473. ⟨hal-00545051⟩