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.

中文翻译：

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动态各向异性薛定ding方程中出现的随时间变化的电磁势的Hölder稳定恢复

我们考虑到Dirichlet-to-Neumann映射的知识，在边界为$ n \ geq2 $的简单黎曼流形上稳定确定Schrödinger方程的时间和空间相关系数的Hölder反问题。假设磁势的发散是已知的，我们表明可以从这些数据中稳定地恢复到电势和磁势。在这里，我们还删除了先前结果中存在的磁势螺线管部分的小假设。