On single measurement stability for the fractional Calderón problem
In this short article we complement the known single measurement uniqueness result for the fractional Calderón problem by a single measurement logarithmic stability estimate. To this end, we combine quantitative propagation of smallness results for the Caffarelli--Silvestre extension and a boundary...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
September 14, 2021
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| In: |
SIAM journal on mathematical analysis
Year: 2021, Volume: 53, Issue: 5, Pages: 5094-5113 |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/20M1381964 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/20M1381964 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/20M1381964 
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| Author Notes: | Angkana Rüland |
| Summary: | In this short article we complement the known single measurement uniqueness result for the fractional Calderón problem by a single measurement logarithmic stability estimate. To this end, we combine quantitative propagation of smallness results for the Caffarelli--Silvestre extension and a boundary doubling estimate. The latter yields control of the order of vanishing of solutions to the fractional Schrödinger equation and provides the central step in passing from the quantitative unique continuation for solutions to the logarithmic stability of the potential $q$. |
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| Item Description: | Gesehen am 23.02.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/20M1381964 |