The higher order fractional Calderón problem for linear local operators: Uniqueness
We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the exterior Dirichle...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
21 February 2022
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| In: |
Advances in mathematics
Year: 2022, Volume: 399, Pages: 1-29 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2022.108246 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.aim.2022.108246 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0001870822000627 
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| Author Notes: | Giovanni Covi, Keijo Mönkkönen, Jesse Railo, Gunther Uhlmann |
| Summary: | We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that one can uniquely recover the coefficients of the PDO from the exterior Dirichlet-to-Neumann (DN) map associated to the perturbed FSE. This is proved for two classes of coefficients: coefficients which belong to certain spaces of Sobolev multipliers and coefficients which belong to fractional Sobolev spaces with bounded derivatives. Our study generalizes recent results for the zeroth and first order perturbations to higher order perturbations. |
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| Item Description: | Gesehen am 28.06.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2022.108246 |