In this article we study the stability in an inverse problem of recovering the magnetic field and the electric potential in a bounded smooth domain from boundary observation of the corresponding wave equation. We prove that the knowledge of the partial Dirichlet-to-Neumann map measured on arbitrary subset of the boundary determines the electric potential and the magnetic field. Next, we apply this result to prove the uniqueness for the multidimensional Borg–Levinson theorem for the electro-magnetic potential from partial data.

中文翻译：

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电磁波方程的部分数据逆问题及其在相关的Borg-Levinson定理中的应用

在本文中，我们将从相应波动方程的边界观测中研究在有界光滑域中恢复磁场和电势的反问题的稳定性。我们证明，在边界的任意子集上测得的局部Dirichlet-Neumann映射的知识决定了电势和磁场。接下来，我们应用此结果来证明多维Borg-Levinson定理对于来自部分数据的电磁势的唯一性。