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dc.contributor.authorCekić, Mihajlo
dc.contributor.authorLin, Yi-Hsuan
dc.contributor.authorRüland, Angkana
dc.date.accessioned2020-05-18T09:22:21Z
dc.date.available2020-05-18T09:22:21Z
dc.date.issued2020
dc.identifier.citationCekić, M., Lin, Y.-H., & Rüland, A. (2020). The Calderón problem for the fractional Schrödinger equation with drift. <i>Calculus of Variations and Partial Differential Equations</i>, <i>59</i>(3), Article 91. <a href="https://doi.org/10.1007/s00526-020-01740-6" target="_blank">https://doi.org/10.1007/s00526-020-01740-6</a>
dc.identifier.otherCONVID_35417937
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/69010
dc.description.abstractWe investigate the Calderón problem for the fractional Schrödinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does not enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many generic measurements is discussed. Here the genericity is obtained through singularity theory which might also be interesting in the context of hybrid inverse problems. Combined with the results from Ghosh et al. (Uniqueness and reconstruction for the fractional Calderón problem with a single easurement, 2018. arXiv:1801.04449), this yields a finite measurements constructive reconstruction algorithm for the fractional Calderón problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension n≥ 1.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesCalculus of Variations and Partial Differential Equations
dc.rightsCC BY 4.0
dc.titleThe Calderón problem for the fractional Schrödinger equation with drift
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202005183265
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn0944-2669
dc.relation.numberinseries3
dc.relation.volume59
dc.type.versionpublishedVersion
dc.rights.copyright© The Authors 2020
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber309963
dc.subject.ysoinversio-ongelmat
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s00526-020-01740-6
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationOpen access funding provided by Projekt DEAL. This project strongly profited from many discussions among the authors during the HIM summer school “Unique continuation and inverse problems” and the MPI MIS summer school “Inverse and Spectral Problems for (Non)-Local Operators” at which the authors participated. The authors would like to thank that Hausdorff Center for Mathematics and the Max-Planck Institute for Mathematics in the Sciences for their support during these two weeks. YHL was supported by the Academy of Finland, under the Project Number 309963, 2018–2019. YHL is now supported by the Ministry of Science and Technology Taiwan, under the Columbus Program: MOST-109-2636-M-009-006, 2020–2025. In the course of writing of this work, MC was supported by the Max-Planck Institute for Mathematics in Bonn. MC is currently supported by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant Agreement No. 725967).
dc.type.okmA1


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