Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains

Yavar Kian (1) , Quang Sang Phan (2) , Eric Soccorsi (1)

1 CPT - Centre de Physique Théorique - UMR 7332
2 Institute of Mathematics [Krakow]

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schrödinger equation in an infinite cylindrical domain from one boundary Neumann observation of the solution. We prove Hölder stability by choosing the Dirichlet boundary condition suitably.

Mots clés: Carleman estimate; Schrödinger equation; scalar potential; Inverse problem; infinite cylindrical domain

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian, Quang Sang Phan, Eric Soccorsi. Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains. Journal of Mathematical Analysis and Applications, 2015, 426 (1), pp.194-210. ⟨10.1016/j.jmaa.2015.01.028⟩. ⟨hal-00907141⟩