Stability estimate in an inverse problem for non-autonomous Schrödinger equations

Michel Cristofol (1, 2, 3, 4) , Eric Soccorsi (5)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université
3 CNRS - Centre National de la Recherche Scientifique
4 ECM - École Centrale de Marseille
5 CPT - Centre de Physique Théorique - UMR 7332

We consider the inverse problem of determining the time dependent magnetic field of the Schrödinger equation in a bounded open subset of $R^n$, with $n \geq 1$, from a finite number of Neumann data, when the boundary measurement is taken on an appropriate open subset of the boundary. We prove the Lispchitz stability of the magnetic potential in the Coulomb gauge class by $n$ times changing initial value suitably.

Domaines: Equations aux dérivées partielles [math.AP]

Michel Cristofol, Eric Soccorsi. Stability estimate in an inverse problem for non-autonomous Schrödinger equations. Applicable Analysis, 2011, 90 (10), pp.1499-1520. ⟨hal-00735593⟩