Uniqueness for the fractional Calderón problem with quasilocal perturbations
We study the fractional Schrödinger equation with quasilocal perturbations and show that the qualitative unique continuation and Runge approximation properties hold in the assumption of sufficient decay. Quantitative versions of both results are also obtained via a propagation of smallness analysis...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2022
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| In: |
SIAM journal on mathematical analysis
Year: 2022, Volume: 54, Issue: 6, Pages: 6136-6163 |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/22M1478641 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/22M1478641 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/22M1478641 
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| Author Notes: | Giovanni Covi |
| Summary: | We study the fractional Schrödinger equation with quasilocal perturbations and show that the qualitative unique continuation and Runge approximation properties hold in the assumption of sufficient decay. Quantitative versions of both results are also obtained via a propagation of smallness analysis for the Caffarelli--Silvestre extension. The results are then used to show uniqueness in the inverse problem of retrieving a quasilocal perturbation from Dirichlet-to-Neumann (DN) data under suitable geometric assumptions. Our work generalizes recent results regarding the locally perturbed fractional Calderón problem. |
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| Item Description: | Gesehen am 16.05.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1095-7154 |
| DOI: | 10.1137/22M1478641 |