Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation

Yavar Kian (1, 2) , Eric Soccorsi (2, 1)

1 CPT - E8 Dynamique quantique et analyse spectrale
2 CPT - Centre de Physique Théorique - UMR 7332

We consider the inverse problem of determining the time and space dependent electromagnetic potential of the Schrödinger equation in a bounded domain of R n , n 2, by boundary observation of the solution over the entire time span. Assuming that the divergence of the magnetic potential is fixed, we prove that the electric potential and the magnetic potential can be Hölder stably retrieved from these data, whereas stability estimates for inverse time-dependent coefficients problems of evolution partial differential equations are usually of logarithmic type.

Mots clés: Schrödinger equation; time-dependent electromagnetic potential; stability estimate; Inverse problem

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian, Eric Soccorsi. Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation. SIAM Journal on Mathematical Analysis, 2019, 51 (2), pp.627-647. ⟨10.1137/18M1197308⟩. ⟨hal-01517497⟩