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The Calderón problem for the fractional Schrödinger equation

dc.contributor.authorGhosh, Tuhin
dc.contributor.authorSalo, Mikko
dc.contributor.authorUhlmann, Gunther
dc.date.accessioned2020-03-20T08:40:29Z
dc.date.available2020-03-20T08:40:29Z
dc.date.issued2020
dc.identifier.citationGhosh, T., Salo, M., & Uhlmann, G. (2020). The Calderón problem for the fractional Schrödinger equation. <i>Analysis and PDE</i>, <i>13</i>(2), 455-475. <a href="https://doi.org/10.2140/apde.2020.13.455" target="_blank">https://doi.org/10.2140/apde.2020.13.455</a>
dc.identifier.otherCONVID_35078766
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/68259
dc.description.abstractWe show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension ≥1 and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calderón problem.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherMathematical Sciences Publishers
dc.relation.ispartofseriesAnalysis and PDE
dc.rightsIn Copyright
dc.subject.otherinverse problem
dc.subject.otherCalderón problem
dc.subject.otherfractional Laplacian
dc.subject.otherapproximation property
dc.titleThe Calderón problem for the fractional Schrödinger equation
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202003202485
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange455-475
dc.relation.issn2157-5045
dc.relation.numberinseries2
dc.relation.volume13
dc.type.versionpublishedVersion
dc.rights.copyright© 2020 Mathematical Sciences Publishers
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber284715 HY
dc.relation.grantnumber309963
dc.relation.grantnumber307023
dc.relation.grantnumber307023
dc.relation.grantnumber770924
dc.relation.grantnumber770924
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/307023/EU//InvProbGeomPDE
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified
dc.subject.ysoapproksimointi
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysoinversio-ongelmat
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p4982
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.2140/apde.2020.13.455
dc.relation.funderResearch Council of Finlanden
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
dc.relation.funderEuropean Commissionen
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderEuroopan komissiofi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramFP7 (EU's 7th Framework Programme)en
jyx.fundingprogramERC Consolidator Granten
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramEU:n 7. puiteohjelma (FP7)fi
jyx.fundingprogramERC Consolidator Grantfi
jyx.fundinginformationSalo was partly supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963) and by the European Research Council under FP7/2007-2013 (ERC StG 307023) and Horizon 2020 (ERC CoG 770924). Uhlmann was partly supported by the NSF, a Si-Yuan Professorship at IAS, HKUST, and a FiDiPro at the University of Helsinki.
dc.type.okmA1


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