The fractional Calderón problem: low regularity and stability
The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inv...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
21 Aug 2017
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| In: |
Arxiv
Year: 2017, Pages: 1-64 |
| DOI: | 10.1016/j.na.2019.05.010 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.na.2019.05.010 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1708.06294 
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| Verfasserangaben: | Angkana Rüland and Mikko Salo |
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| 520 | |a The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant $L^p$ or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli-Silvestre extension and a duality argument. | ||
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