Uniqueness for the fractional Calderón problem with quasilocal perturbations

• Verfasst von: Covi, Giovanni [VerfasserIn]
• Titel: Uniqueness for the fractional Calderón problem with quasilocal perturbations
• Verf.angabe: Giovanni Covi
• Jahr: 2022
• Umfang: 28 S.
• Fussnoten: Gesehen am 16.05.2023
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on mathematical analysis
• Ort Quelle: Philadelphia, Pa. : SIAM, 1970
• Jahr Quelle: 2022
• Band/Heft Quelle: 54(2022), 6, Seite 6136-6163
• ISSN Quelle: 1095-7154
• DOI: doi:10.1137/22M1478641
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1845503716

Abstract

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.