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Status: Bibliographieeintrag

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Verfasst von:Covi, Giovanni [VerfasserIn]   i
 García-Ferrero, María Ángeles [VerfasserIn]   i
 Rüland, Angkana [VerfasserIn]   i
Titel:On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
Verf.angabe:Giovanni Covi, María Ángeles García-Ferrero, Angkana Rüland
E-Jahr:2022
Jahr:25 December 2022
Umfang:71 S.
Fussnoten:Online verfügbar: 20. September 2022 ; Gesehen am 14.02.2023
Titel Quelle:Enthalten in: Journal of differential equations
Ort Quelle:Orlando, Fla. : Elsevier, 1965
Jahr Quelle:2022
Band/Heft Quelle:341(2022), Seite 79-149
ISSN Quelle:1090-2732
Abstract:In this article we consider direct and inverse problems for α-stable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structural condition of directional antilocality as introduced by Y. Ishikawa in the 80s. We consider the Dirichlet problem for these operators on the respective “domain of dependence of the operator” and in several, adapted function spaces. This formulation allows one to avoid natural “gauges” which would else have to be considered in the study of the associated inverse problems. Exploiting the directional antilocality of these operators we complement the investigation of the direct problem with infinite data and single measurement uniqueness results for the associated inverse problems. Here, due to the only directional antilocality, new geometric conditions arise on the measurement domains. We discuss both the setting of symmetric and a particular class of non-symmetric nonlocal elliptic operators, and contrast the corresponding results for the direct and inverse problems. In particular for only “one-sided operators” new phenomena emerge both in the direct and inverse problems: For instance, it is possible to study the problem in data spaces involving local and nonlocal data, the unique continuation property may not hold in general and further restrictions on the measurement set for the inverse problem arise.
DOI:doi:10.1016/j.jde.2022.09.009
URL:Bitte beachten Sie: Dies ist ein Bibliographieeintrag. Ein Volltextzugriff für Mitglieder der Universität besteht hier nur, falls für die entsprechende Zeitschrift/den entsprechenden Sammelband ein Abonnement besteht oder es sich um einen OpenAccess-Titel handelt.

Volltext: https://doi.org/10.1016/j.jde.2022.09.009
 Volltext: https://www.sciencedirect.com/science/article/pii/S0022039622005344
 DOI: https://doi.org/10.1016/j.jde.2022.09.009
Datenträger:Online-Ressource
Sprache:eng
Sach-SW:Directional antilocality
 Inverse problem
 Nonlocal operators
K10plus-PPN:1835119956
Verknüpfungen:→ Zeitschrift

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