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...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
7 February 2020
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| In: |
Journal of functional analysis
Year: 2020, Volume: 279, Issue: 1, Pages: 1-42 |
| ISSN: | 1096-0783 |
| DOI: | 10.1016/j.jfa.2020.108505 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jfa.2020.108505 Verlag, lizenzpflichtig, Volltext: https://jyx.jyu.fi/handle/123456789/68537 
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| Author Notes: | Tuhin Ghosh, Angkana Rüland, Mikko Salo, Gunther Uhlmann |
| 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. |
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| Item Description: | Gesehen am 19.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1096-0783 |
| DOI: | 10.1016/j.jfa.2020.108505 |