Stable determination of coefficients in the dynamical Schr\"odinger equation in a magnetic field

Mourad Bellassoued

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arXiv · 1510.04247

Stable determination of coefficients in the dynamical Schr\"odinger equation in a magnetic field

Mourad Bellassoued

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Abstract

In this paper we consider the inverse problem of determining on a compact Riemannian manifold the electric potential or the magnetic field in a Schr\"odinger equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the magnetic Schr\"odinger equation. We prove that the knowledge of the Dirichlet-to-Neumann map for the Schr\"odinger equation uniquely determines the magnetic field and the electric potential and we establish H\"older-type stability.

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Mourad Bellassoued. 2015-10-14. Stable determination of coefficients in the dynamical Schr\"odinger equation in a magnetic field. https://arxiv.org/abs/1510.04247

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