Reconstruction of the potential from partial Cauchy data for the Schroedinger equation
Reconstruction of the potential from partial Cauchy data for the Schroedinger equation
复制标题
DOI：
10.1512/iumj.2004.53.2299
复制
发表时间：
2004
影响因子：
1.1
通讯作者：
H. Ammari;G. Uhlmann
中科院分区：
文献类型：
--
作者：
H. Ammari;G. Uhlmann
本文证明了在d ≥ 3维情形下，当q在边界邻域内已知时，薛定谔方程在边界的任意开子集Γ上的部分Cauchy数据的知识唯一地确定了势q.我们还推导出一个公式，用于计算从部分Dirichlet到Neumann映射的潜在的q。我们应用的方法来确定位置的小体积分数扰动的潜在的（或折射率）的非均匀介质的边界上进行局部测量。
In this paper we prove in dimension d ≥ 3 that the knowledge of the partial Cauchy data for the Schrodinger equation on any open subset Γ of the boundary determines uniquely the potential q provided that q is known in a neighborhood of the boundary. We also derive a formula for calculating the potential q from the partial Dirichlet to Neumann map associated to q. We apply the methods to identify locations of small volume fraction perturbations of the potential (or the index of refraction) of inhomogeneous media by making local measurements on the boundary.