Calderon's inverse conductivity problem in the plane
Calderon's inverse conductivity problem in the plane
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DOI：
10.4007/annals.2006.163.265
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发表时间：
2006-01-01
影响因子：
4.9
通讯作者：
Paivarinta, Lassi
中科院分区：
文献类型：
--
作者：
Astala, Kari;Paivarinta, Lassi
我们证明，二维域中方程 del center dot sigma del u = 0 的狄利克雷到诺依曼映射唯一地确定了有界可测量电导率 a。这对 A. P. Calderon 1980 年提出的问题给出了肯定的答案。早些时候，仅针对足够平滑的电导率显示了结果。在更高维度中，这个问题仍然悬而未决。
We show that the Dirichlet to Neumann map for the equation del center dot sigma del u = 0 in a two-dimensional domain uniquely determines the bounded measurable conductivity a. This gives a positive answer to a question of A. P. Calderon from 1980. Earlier the result has been shown only for conductivities that are sufficiently smooth. In higher dimensions the problem remains open.