分数阶 Calderón 问题在单次测量下的唯一性与重构
偏微分方程分析
2020-02-12 v3
摘要
我们证明了分数阶 Calderón 问题在单次测量下以及数据位于外部任意（可能不相交）子集上的整体唯一性。先前的工作 \cite{GhoshSaloUhlmann} 考虑了无穷多次测量的情形。该方法同样基于分数阶方程的强唯一性性质，此次结合了对零测集的唯一延拓原理。我们还给出了一种由单次外部测量确定未知势的构造性步骤，其基于涉及不同正则化方案的该唯一延拓结果的构造性版本。
关键词
引用
@article{arxiv.1801.04449,
title = {Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement},
author = {Tuhin Ghosh and Angkana Rüland and Mikko Salo and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1801.04449},
year = {2020}
}
备注
32 pages, is a slightly updated version, Accepted Manuscript for Journal of Functional Analysis, volume and pages to be assigned by Elsevier, DOI:10.1016/j.jfa.2020.108505. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0