Stability estimates for an inverse scattering problem at high frequencies

Habib Ammari (1) , Hajer Bahouri (2) , David dos Santos Ferreira (3) , Isabelle Gallagher (4)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 LAGA - Laboratoire Analyse, Géométrie et Applications
4 IMJ - Institut de Mathématiques de Jussieu

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that, in the case of a radial potential supported sufficiently near the boundary, infinite resolution can be achieved from measurements of the near-field operator in the monotone case.

Domaines: Equations aux dérivées partielles [math.AP]

Habib Ammari, Hajer Bahouri, David dos Santos Ferreira, Isabelle Gallagher. Stability estimates for an inverse scattering problem at high frequencies. 2012. ⟨hal-00702325⟩