On single measurement stability for the fractional Calderón problem
In this short note we prove the logarithmic stability of the single measurement uniqueness result for the fractional Calder\'on problem which had been derived in \cite{GRSU18}. To this end, we use the quantitative uniqueness results established in \cite{RS20a} and complement these bounds with a...
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| Main Author: | |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
27 Jul 2020
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| In: |
Arxiv
Year: 2020, Pages: 1-16 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2007.13624
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| Author Notes: | Angkana Rüland |
| Summary: | In this short note we prove the logarithmic stability of the single measurement uniqueness result for the fractional Calder\'on problem which had been derived in \cite{GRSU18}. To this end, we use the quantitative uniqueness results established in \cite{RS20a} and complement these bounds with a boundary doubling estimate. The latter yields control of the order of vanishing of solutions to the fractional Schr\"odinger equation. Then, following a scheme introduced in \cite{S10,ASV13} in the context of the determination of a surface impedance from far field measurements, this allows us to deduce logarithmic stability of the potential $q$. |
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| Item Description: | Last revised 21 Nov 2020 (v2) Gesehen am 27.05.2021 |
| Physical Description: | Online Resource |