Strong unique continuation for the higher order fractional Laplacian

• Verfasst von: García-Ferrero, María Ángeles [VerfasserIn]
• Verfasst von: Rüland, Angkana [VerfasserIn]
• Titel: Strong unique continuation for the higher order fractional Laplacian
• Verf.angabe: María-Ángeles García-Ferrero and Angkana Rüland
• E-Jahr: 2019
• Jahr: 26 Feb 2019
• Umfang: 50 S.
• Teil: year:2019
• Teil: elocationid:1902.09851
• Teil: pages:1-50
• Teil: extent:50
• Fussnoten: Gesehen am 12.05.2021
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2019
• Band/Heft Quelle: (2019), Artikel-ID 1902.09851, Seite 1-50
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematics - Analysis of PDEs
• K10plus-PPN: 175775699X

Abstract

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.