Energy and regularity dependent stability estimates for the Gel'fand inverse problem in multidimensions

Mikhail Isaev (1) , Roman Novikov (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We prove new global Hölder-logarithmic stability estimates for the Gel'fand inverse problem at fixed energy in dimension $d\geq 3$. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. Comparisons with preceeding results in this direction are given.

Domaines: Equations aux dérivées partielles [math.AP]

Mikhail Isaev, Roman Novikov. Energy and regularity dependent stability estimates for the Gel'fand inverse problem in multidimensions. Journal of Inverse and Ill-posed Problems, 2012, 20 (3), pp.313-325. ⟨hal-00689636⟩