A partial data result for the magnetic Schrödinger inverse problem
A partial data result for the magnetic Schrödinger inverse problem
复制标题
磁薛定谔逆问题的部分数据结果
DOI：
10.2140/apde.2014.7.117
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发表时间：
2011
期刊：
影响因子：
2.2
通讯作者：
Francis J. Chung
中科院分区：
文献类型：
--
作者：
Francis J. Chung
本文证明了Dos Santos Ferreira，Kenig，Sj“o Strand和Uhlmann等人在边界的某些子集上的Dirichlet-Neumann映射的知识可以用来确定一个磁性Schr‘’o dinger算子.在区域上有一些几何条件的情况下，Dirichlet-Neumann映射的子集或输入函数所支持的子集可以是任意小的.这是对Dos Santos Ferreira，Kenig，Sj”{o}strand和Uhlmann在一篇论文中部分数据结果的改进.该方法通过与由拟微分片建立的算子共轭来修正那篇文章中的Carleman估计。
This article shows that knowledge of the Dirichlet-Neumann map on certain subsets of the boundary for input functions supported roughly on the rest of the boundary can be used to determine a magnetic Schr\"{o}dinger operator. With some geometric conditions on the domain, either the subset on which the DN map is measured or the subset on which the input functions have support may be made arbitrarily small. This is an improvement on the partial data result in a paper by Dos Santos Ferreira, Kenig, Sj\"{o}strand, and Uhlmann. The method involves modifying the Carleman estimate in that paper by conjugation with operators built from pseudodifferential pieces.