Uniqueness and reconstruction for the fractional Calderón problem with a single measurement
We show global uniqueness in the fractional Calder\'on 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...
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| Main Authors: | , , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
13 Jan 2018
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| In: |
Arxiv
Year: 2018, Pages: 1-32 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1801.04449
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| Author Notes: | Tuhin Ghosh, Angkana Rüland, Mikko Salo, and Gunther Uhlmann |
| Summary: | We show global uniqueness in the fractional Calder\'on 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. |
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| Item Description: | Gesehen am 19.05.2021 |
| Physical Description: | Online Resource |