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arXiv · 1903.07039

Stable determination of a vector field in a non-self-adjoint dynamical Schr\"odinger equation on Riemannian manifolds

Mourad Bellassoued·Ibtissem Ben Aïcha·Zouhour Rezig
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Abstract

This paper deals with an inverse problem for a non-self-adjoint Schr\"odinger equation on a compact Riemannian manifold. Our goal is to stably determine a real vector field from the dynamical Dirichlet-to Neumann map. We establish in dimension n greater than 2, an H\"older type stability estimate for the inverse problem under study. The proof is mainly based on the reduction to an equivalent problem for an electro-magnetic Schr\"odinger equation and the use of a Carleman estimate designed for elliptic operators.

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Mourad Bellassoued, Ibtissem Ben Aïcha, Zouhour Rezig. 2019-03-17. Stable determination of a vector field in a non-self-adjoint dynamical Schr\"odinger equation on Riemannian manifolds. https://arxiv.org/abs/1903.07039

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