有界磁势磁Schrödinger算子反边界问题的唯一性
偏微分方程分析
2012-07-10 v2 数学物理
math.MP
摘要
我们证明，对于磁势和电势的磁Schrödinger算子，在（）中有界开集边界上的Cauchy数据集合的知识唯一地决定了集合内部的磁场和电势。证明基于一个具有两阶导数增益的磁Schrödinger算子的Carleman估计。
引用
@article{arxiv.1206.4727,
title = {Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential},
author = {Katsiaryna Krupchyk and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1206.4727},
year = {2012}
}
备注
This version contains a slight generalization of the main result of the previous version, with a complete proof. It supersedes the preprint http://arxiv.org/abs/1205.1151