The Calderón problem for the fractional Schrödinger equation
| dc.contributor.author | Ghosh, Tuhin | |
| dc.contributor.author | Salo, Mikko | |
| dc.contributor.author | Uhlmann, Gunther | |
| dc.date.accessioned | 2020-03-20T08:40:29Z | |
| dc.date.available | 2020-03-20T08:40:29Z | |
| dc.date.issued | 2020 | |
| dc.identifier.citation | Ghosh, 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.other | CONVID_35078766 | |
| dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/68259 | |
| dc.description.abstract | We 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.mimetype | application/pdf | |
| dc.language | eng | |
| dc.language.iso | eng | |
| dc.publisher | Mathematical Sciences Publishers | |
| dc.relation.ispartofseries | Analysis and PDE | |
| dc.rights | In Copyright | |
| dc.subject.other | inverse problem | |
| dc.subject.other | Calderón problem | |
| dc.subject.other | fractional Laplacian | |
| dc.subject.other | approximation property | |
| dc.title | The Calderón problem for the fractional Schrödinger equation | |
| dc.type | article | |
| dc.identifier.urn | URN:NBN:fi:jyu-202003202485 | |
| dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
| dc.contributor.laitos | Department of Mathematics and Statistics | en |
| dc.contributor.oppiaine | Inversio-ongelmien huippuyksikkö | fi |
| dc.contributor.oppiaine | Matematiikka | fi |
| dc.contributor.oppiaine | Centre of Excellence in Inverse Problems | en |
| dc.contributor.oppiaine | Mathematics | en |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
| dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
| dc.description.reviewstatus | peerReviewed | |
| dc.format.pagerange | 455-475 | |
| dc.relation.issn | 2157-5045 | |
| dc.relation.numberinseries | 2 | |
| dc.relation.volume | 13 | |
| dc.type.version | publishedVersion | |
| dc.rights.copyright | © 2020 Mathematical Sciences Publishers | |
| dc.rights.accesslevel | openAccess | fi |
| dc.relation.grantnumber | 284715 HY | |
| dc.relation.grantnumber | 309963 | |
| dc.relation.grantnumber | 307023 | |
| dc.relation.grantnumber | 307023 | |
| dc.relation.grantnumber | 770924 | |
| dc.relation.grantnumber | 770924 | |
| dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/307023/EU//InvProbGeomPDE | |
| dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified | |
| dc.subject.yso | approksimointi | |
| dc.subject.yso | osittaisdifferentiaaliyhtälöt | |
| dc.subject.yso | inversio-ongelmat | |
| dc.format.content | fulltext | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p4982 | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p12392 | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p27912 | |
| dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
| dc.relation.doi | 10.2140/apde.2020.13.455 | |
| dc.relation.funder | Research Council of Finland | en |
| dc.relation.funder | Research Council of Finland | en |
| dc.relation.funder | European Commission | en |
| dc.relation.funder | European Commission | en |
| dc.relation.funder | Suomen Akatemia | fi |
| dc.relation.funder | Suomen Akatemia | fi |
| dc.relation.funder | Euroopan komissio | fi |
| dc.relation.funder | Euroopan komissio | fi |
| jyx.fundingprogram | Centre of Excellence, AoF | en |
| jyx.fundingprogram | Academy Project, AoF | en |
| jyx.fundingprogram | FP7 (EU's 7th Framework Programme) | en |
| jyx.fundingprogram | ERC Consolidator Grant | en |
| jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
| jyx.fundingprogram | Akatemiahanke, SA | fi |
| jyx.fundingprogram | EU:n 7. puiteohjelma (FP7) | fi |
| jyx.fundingprogram | ERC Consolidator Grant | fi |
| jyx.fundinginformation | Salo 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.okm | A1 |
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