Hölder Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schrödinger Equation

Yavar Kian (1, 2) , Alexander Tetlow (3)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E8 Dynamique quantique et analyse spectrale
3 UCL - University College of London [London]

We consider the inverse problem of Höldder-stably determining the time-and space-dependent coefficients of the Schrödinger equation on a simple Riemannian manifold with boundary of dimension n ≥ 2 from knowledge of the Dirichlet-to-Neumann map. Assuming the divergence of the magnetic potential is known, we show that the electric and magnetic potentials can be Hölder-stably recovered from these data. Here we also remove the smallness assumption for the solenoidal part of the magnetic potential present in previous results.

Domaines: Equations aux dérivées partielles [math.AP]

Yavar Kian, Alexander Tetlow. Hölder Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schrödinger Equation. Inverse Problems and Imaging , 2020, 14 (5), pp.819-839. ⟨10.3934/ipi.2020038⟩. ⟨hal-02073349⟩