We are concerned with the Calderon problem of determining an unknown conductivity of a body from the associated boundary measurement. We establish a logarithmic type stability estimate in terms of the Hausdorff distance in determining the support of a convex polygonal inclusion by a single partial boundary measurement. We also derive the uniqueness result in a more general scenario where the conductivities are piecewise constants supported in a nested polygonal geometry. Our methods in establishing the stability and uniqueness results have a significant technical initiative and a strong potential to apply to other inverse boundary value problems.

中文翻译：

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Calder\'on 问题中多边形夹杂物的单次局部边界测量的稳定确定

我们关注从相关边界测量确定物体的未知电导率的卡尔德隆问题。我们根据 Hausdorff 距离建立对数类型稳定性估计，以通过单个部分边界测量来确定凸多边形包含物的支持。我们还在更一般的情况下得出唯一性结果，其中电导率是嵌套多边形几何中支持的分段常数。我们建立稳定性和唯一性结果的方法具有重要的技术创新性，并且具有应用于其他逆边值问题的强大潜力。