Carleman inequalities and inverse problems for the Schrödinger equation

Alberto Mercado (1) , Axel Osses (2) , Lionel Rosier (3, 4)

1 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]
2 DIMEC - Departamento de Ingeniería Mecánica
3 IECN - Institut Élie Cartan de Nancy
4 CORIDA - Robust control of infinite dimensional systems and applications

In this Note, we derive new Carleman inequalities for the evolution Schrödinger equation under a weak pseudoconvexity condition, which allows us to use weights with a linear spatial dependence. As a result, less restrictive boundary or internal observation regions may be used to obtain the stability for the inverse problem consisting in retrieving a stationary potential in the Schrödinger equation from a single boundary or internal measurement, respectively.

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Alberto Mercado, Axel Osses, Lionel Rosier. Carleman inequalities and inverse problems for the Schrödinger equation. Comptes Rendus. Mathématique, 2008, 346 (1-2), pp.53-58. ⟨10.1016/j.crma.2007.11.014⟩. ⟨hal-00600668⟩