In this paper we are interested in inverse inclusion problem in the plane. We derive uniqueness and Holder stability results of the inclusion recovery problem using a single boundary measurement, under the assumption that the inclusion has a circular shape. We also propose a simple minimizing scheme for the recovery of a disk. Our numerical results show that the Holder power in the stability estimate is close to one.

中文翻译：

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逆包含问题：一种确定磁盘的稳定方法

在本文中，我们对平面中的逆包含问题感兴趣。在夹杂物具有圆形形状的假设下，我们使用单个边界测量推导出夹杂物恢复问题的唯一性和 Holder 稳定性结果。我们还提出了一种用于恢复磁盘的简单最小化方案。我们的数值结果表明稳定性估计中的 Holder power 接近于 1。