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: 20 August 2019
• Umfang: 60 S.
• Teil: volume:1
• Teil: year:2019
• Teil: number:4
• Teil: pages:715-774
• Teil: extent:60
• Fussnoten: Gesehen am 12.05.2021
• Titel Quelle: Enthalten in: Mathematics in engineering
• Ort Quelle: Springfield, MO : AIMS Press, 2019
• Jahr Quelle: 2019
• Band/Heft Quelle: 1(2019), 4, Seite 715-774
• ISSN Quelle: 2640-3501
• DOI: doi:10.3934/mine.2019.4.715
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 175775704X

Abstract

In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schrödinger 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 Calderón 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.