Title: Reconstruction in the Calderón problem on a fixed partition from finite and partial boundary data Show Chinese title

Title: 从有限和部分边界数据中在固定划分上的Calderón问题的重构

Abstract: This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118--1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a layering assumption and the local Neumann-to-Dirichlet map was needed since the piecewise constant partitioning also was assumed unknown. Here I show how to modify the method in case the partitioning is known, for general piecewise constant conductivities and only a finite number of partial boundary measurements. Moreover, no lower/upper bounds on the unknown conductivity are needed. Show Chinese abstract

Abstract: 此简短注释修改了作者（Comm. PDE, 45(9):1118--1133, 2020）提出的重建方法，用于在Calderón问题（电学阻抗断层扫描）中重建分段常数电导率。在之前的文章中，由于假设分段常数分割也是未知的，因此需要分层假设和局部Neumann-to-Dirichlet映射。在这里，我展示了如何在分割已知的情况下修改该方法，适用于一般的分段常数电导率，并且仅需要有限数量的部分边界测量。此外，不需要未知电导率的下界/上界。