Hölder-stable recovery of time-dependent electromagnetic potentials appearing in a dynamical anisotropic Schrödinger equation

Yavar Kian; Alexander Tetlow

doi:10.3934/ipi.2020038

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2020, Volume 14, Issue 5: 819-839. Doi: 10.3934/ipi.2020038

This issue Previous Article Numerical recovery of magnetic diffusivity in a three dimensional spherical dynamo equation Next Article Stability estimates for time-dependent coefficients appearing in the magnetic Schrödinger equation from arbitrary boundary measurements

Hölder-stable recovery of time-dependent electromagnetic potentials appearing in a dynamical anisotropic Schrödinger equation

Yavar Kian^1, and
Alexander Tetlow^2,

1.
Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
2.
Department of Mathematics, University College London, London, UK

Y. Kian was partially supported by the Agence Nationale de la Recherche under grant ANR-17-CE40-0029.

Received: October 31, 2019

Revised: February 29, 2020

Published: July 2020

A. Tetlow was supported by EPSRC DTP studentship EP/N509577/1

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Abstract

We consider the inverse problem of Hölder-stably determining the time- and space-dependent coefficients of the Schrödinger equation on a simple Riemannian manifold with boundary of dimension $ n\geq2 $ from the 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.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35R01.

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