A Holder-logarithmic stability estimate for an inverse problem in two dimensions - Département de mathématiques appliquées Accéder directement au contenu
Article Dans Une Revue Journal of Inverse and Ill-posed Problems Année : 2015

A Holder-logarithmic stability estimate for an inverse problem in two dimensions

Résumé

The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient increasing stability phenomenon at sufficiently high energies: in some sense, the stability rapidly changes from logarithmic type to Holder type. The paper develops also several estimates for a non-local Riemann-Hilbert problem which could be of independent interest.
Fichier principal
Vignette du fichier
articleV2.pdf (303.67 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00829852 , version 1 (04-06-2013)
hal-00829852 , version 2 (27-06-2013)

Licence

Paternité

Identifiants

Citer

Matteo Santacesaria. A Holder-logarithmic stability estimate for an inverse problem in two dimensions. Journal of Inverse and Ill-posed Problems, 2015, 23 (1), pp.51-73. ⟨10.1515/jiip-2013-0055⟩. ⟨hal-00829852v2⟩
277 Consultations
161 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More