This paper deals with an inverse problem for a non-self-adjoint Schrödinger 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\geq2 $, an Hölder 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 Schrödinger equation and the use of a Carleman estimate designed for elliptic operators.

中文翻译：

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黎曼流形上非自伴动力学薛定ding方程中向量场的稳定确定

本文讨论了紧黎曼流形上一个非自伴Schrödinger方程的逆问题。我们的目标是从动态Dirichlet到Neumann映射稳定地确定一个实矢量场。我们在维度$ n \ geq2 $中建立了研究中反问题的Hölder类型稳定性估计。证明主要基于将电磁Schrödinger方程的等价问题简化并使用为椭圆算子设计的Carleman估计。