On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols

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 t...

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Detalles Bibliográficos
Autores: Covi, G., García-Ferrero, M.A., Rüland, A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1553
Acceso en línea:http://hdl.handle.net/20.500.11824/1553
Access Level:acceso embargado
Palabra clave:Directional antilocality
Inverse problem
Nonlocal operators
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spelling On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbolsCovi, G.García-Ferrero, M.A.Rüland, A.Directional antilocalityInverse problemNonlocal operatorsIn 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.202320232022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1553reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://doi.org/10.1016/j.jde.2022.09.009info:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/embargoedAccessoai:bird.bcamath.org:20.500.11824/15532026-06-19T12:47:47Z
dc.title.none.fl_str_mv On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
title On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
spellingShingle On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
Covi, G.
Directional antilocality
Inverse problem
Nonlocal operators
title_short On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
title_full On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
title_fullStr On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
title_full_unstemmed On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
title_sort On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
dc.creator.none.fl_str_mv Covi, G.
García-Ferrero, M.A.
Rüland, A.
author Covi, G.
author_facet Covi, G.
García-Ferrero, M.A.
Rüland, A.
author_role author
author2 García-Ferrero, M.A.
Rüland, A.
author2_role author
author
dc.subject.none.fl_str_mv Directional antilocality
Inverse problem
Nonlocal operators
topic Directional antilocality
Inverse problem
Nonlocal operators
description 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.
publishDate 2022
dc.date.none.fl_str_mv 2022
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1553
url http://hdl.handle.net/20.500.11824/1553
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.jde.2022.09.009
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/embargoedAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
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dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
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