Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
Ghosh, Tuhin; Rüland, Angkana; Salo, Mikko; Uhlmann, Gunther (2020). Uniqueness and reconstruction for the fractional Calderón problem with a single measurement. Journal of Functional Analysis, 279, 1, 108505. DOI: 10.1016/j.jfa.2020.108505
Published inJournal of Functional Analysis
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© 2020 Elsevier Inc
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  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.
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Academy Project, AoF; FP7 (EU's 7th Framework Programme); Centre of Excellence, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingM.S. was supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 312121 and 309963) and by the European Research Council under FP7/2007-2013 (ERC StG 307023) and Horizon 2020 (ERC CoG 770924). G.U. was partly supported by NSF and a Si-Yuan Professorship at IAS, HKUST.
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