Uniqueness and reconstruction for the fractional Calderon problem with a single measurement

被引：50
|
作者：
Ghosh, Tuhin [1 ]
Rueland, Angkana [2 ]
Salo, Mikko [3 ]
Uhlmann, Gunther [1 ,4 ]
机构：
[1] HKUST, Jockey Club Inst Adv Study, Hong Kong, Peoples R China
[2] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany
[3] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla, Finland
[4] Univ Washington, Dept Math, Seattle, WA 98195 USA
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2020年 / 279卷 / 01期
基金：
欧洲研究理事会; 芬兰科学院;
关键词：
Inverse problems; Calderon problem; Fractional Laplacian; Unique continuation; Single measurement; CONTINUATION; EQUATIONS; DOMAINS;
D O I：
10.1016/j.jfa.2020.108505
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show global uniqueness in the fractional Calderon problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work [10] considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes. (C) 2020 Elsevier Inc. All rights reserved.
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页数：42
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