The fractional Calderón problem: Low regularity and stability
The Calderón problem for the fractional Schrödinger equation was introduced in the work Ghosh et al. (to appear) 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 in...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2020
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| In: |
Nonlinear analysis. Theory, methods & applications
Year: 2019, Volume: 193, Pages: 1-56 |
| ISSN: | 1873-5215 |
| DOI: | 10.1016/j.na.2019.05.010 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.na.2019.05.010 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0362546X19301622 
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| Author Notes: | Angkana Rüland, Mikko Salo |
| Summary: | The Calderón problem for the fractional Schrödinger equation was introduced in the work Ghosh et al. (to appear) 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 Lp 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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| Item Description: | Available online 28 May 2019 Gesehen am 26.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1873-5215 |
| DOI: | 10.1016/j.na.2019.05.010 |