Exponential instability in the inverse scattering problem on the energy interval

Mikhail Isaev (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows optimality of the logarithmic stability result of [Stefanov, 1990] (up to the value of the exponent).

Domaines: Equations aux dérivées partielles [math.AP]

Mikhail Isaev. Exponential instability in the inverse scattering problem on the energy interval. Functional Analysis and Its Applications, 2013, 47 (3), pp.8. ⟨hal-00550233⟩