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

We show global uniqueness in the fractional Calderón 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...

Full description

Saved in:
Bibliographic Details
Published inJournal of functional analysis Vol. 279; no. 1; p. 108505
Main Authors Ghosh, Tuhin, Rüland, Angkana, Salo, Mikko, Uhlmann, Gunther
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.07.2020
Subjects
Calderon problem
Fractional Laplacian
Inverse problems
Single measurement
Unique continuation
Inverse problems
Single measurement
Fractional Laplacian
Unique continuation
Calderon problem
Online AccessGet full text

Cover

More Information
Summary:We show global uniqueness in the fractional Calderón 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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108505