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 in
Journal of Functional AnalysisDate
2020Access restrictions
Embargoed until: 2022-07-16Request copy from author
Copyright
© 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 [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.
Publisher
Academic PressISSN Search the Publication Forum
0022-1236Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/34603700
Metadata
Show full item recordCollections
Related funder(s)
Academy of Finland; European CommissionFunding 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 funding
M.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.License
Related items
Showing items with similar title or keywords.
-
Exponential instability in the fractional Calderón problem
Rüland, Angkana; Salo, Mikko (Institute of Physics, 2018)In this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this ... -
Inverse problems for a fractional conductivity equation
Covi, Giovanni (Pergamon Press, 2020)This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, ... -
The Calderón problem for the fractional Schrödinger equation
Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther (Mathematical Sciences Publishers, 2020)We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness ... -
The higher order fractional Calderón problem for linear local operators : Uniqueness
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther (Elsevier, 2022)We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that ... -
Applications of Microlocal Analysis in Inverse Problems
Salo, Mikko (MDPI AG, 2020)This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, ...