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

Abstract

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 \cite{GhoshSaloUhlmann} 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.

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

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