Strong unique continuation for the higher order fractional Laplacian
In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and critical Hardy type potentials. In the same setting, we...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
26 Feb 2019
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| In: |
Arxiv
Year: 2019, Pages: 1-50 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1902.09851
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| Author Notes: | María-Ángeles García-Ferrero and Angkana Rüland |
| Summary: | In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schr\"odinger operators. We deduce the strong unique continuation property in the presence of subcritical and critical Hardy type potentials. In the same setting, we address the unique continuation property from measurable sets of positive Lebesgue measure. As applications we prove the antilocality of the higher order fractional Laplacian and Runge type approximation theorems which have recently been exploited in the context of nonlocal Calder\'on type problems. As our main tools, we rely on the characterisation of the higher order fractional Laplacian through a generalised Caffarelli-Silvestre type extension problem and on adapted, iterated Carleman estimates. |
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| Item Description: | Gesehen am 12.05.2021 |
| Physical Description: | Online Resource |