Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map

Mourad Choulli (1) , Yavar Kian (2) , Eric Soccorsi (3, 2)

1 IECL - Institut Élie Cartan de Lorraine
2 CPT - Centre de Physique Théorique - UMR 7332
3 CPT - E8 Dynamique quantique et analyse spectrale

We examine the stability issue in the inverse problem of determining a scalar potential appearing in the stationary Schrödinger equation in a bounded domain, from a partial elliptic Dirichlet-to-Neumann map. Namely, the Dirichlet data is imposed on the shadowed face of the boundary of the domain and the Neumann data is measured on its illuminated face. We establish a log log stability estimate for the L2-norm (resp. the H minus 1-norm) of bounded (resp. L2) potentials whose difference is lying in any Sobolev space of order positive order.

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Yavar Kian, Eric Soccorsi. Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map . Bulletin of the South Ural State University, 2015, Mathematical Models and Computer Sciences, 8 (3), pp.78-94. ⟨10.14529/mmp150305⟩. ⟨hal-01098368⟩