The geometrical problem of electrical impedance tomography in the disk

被引：0
|
作者：
Sharafutdinov, V. A. [1 ,2 ]
机构：
[1] Sobolev Inst Math, Novosibirsk, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2011年 / 52卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
electrical impedance tomography; Dirichlet-to-Neumann operator; conformal map; BOUNDARY; MANIFOLDS;
D O I：
10.1134/S0037446606010198
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The geometrical problem of electrical impedance tomography consists of recovering a Riemannian metric on a compact manifold with boundary from the Dirichlet-to-Neumann operator (DNoperator) given on the boundary. We present a new elementary proof of the uniqueness theorem: A Riemannian metric on the two-dimensional disk is determined by its DN-operator uniquely up to a conformal equivalence. We also prove an existence theorem that describes all operators on the circle that are DN-operators of Riemannian metrics on the disk.
引用
收藏
页码：178 / 190
页数：13
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