Hyperbolic geometry and local Dirichlet–Neumann map
Hyperbolic geometry and local Dirichlet–Neumann map
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DOI：
10.1016/j.aim.2003.10.006
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发表时间：
2004-11
影响因子：
1.7
通讯作者：
H. Isozaki;G. Uhlmann
中科院分区：
文献类型：
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作者：
H. Isozaki;G. Uhlmann
我们证明了在三维空间中，如果我们知道薛定谔方程的Dirichlet-to-Neumann（DN）映射，且该映射的势围绕着一个中心位于光滑边界的有界区域的凸船体外的球面的交点，那么我们可以通过适当的测度唯一地确定该势的相应球平均.这允许人们确定在测量DN图的边界附近的电势。类似的结果是有效的电阻抗断层扫描。
We show in three dimensions that if we know the Dirichlet-to-Neumann (DN) map associated to the Schrödinger equation with a potential around the intersection of a sphere centered outside the convex hull of a bounded domain with smooth boundary, we can determine uniquely the corresponding spherical mean of the potential with an appropriate measure. This allows one to determine the potential near the boundary where the DN map is measured. Similar results are valid for electrical impedance tomography.