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dc.contributor.authorCovi, Giovanni
dc.contributor.authorMönkkönen, Keijo
dc.contributor.authorRailo, Jesse
dc.date.accessioned2021-10-28T08:58:28Z
dc.date.available2021-10-28T08:58:28Z
dc.date.issued2021
dc.identifier.citationCovi, G., Mönkkönen, K., & Railo, J. (2021). Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems. <i>Inverse Problems and Imaging</i>, <i>15</i>(4), 641-681. <a href="https://doi.org/10.3934/ipi.2021009" target="_blank">https://doi.org/10.3934/ipi.2021009</a>
dc.identifier.otherCONVID_97817913
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/78405
dc.description.abstractWe prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that one can uniquely recover, up to a gauge, electric and magnetic potentials from the Dirichlet-to-Neumann map associated to the higher order fractional magnetic Schrödinger equation. We also study the higher order fractional Schrödinger equation with singular electric potential. In both cases, we obtain a Runge approximation property for the equation. Furthermore, we prove a uniqueness result for a partial data problem of the d-plane Radon transform in low regularity. Our work extends some recent results in inverse problems for more general operators.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.ispartofseriesInverse Problems and Imaging
dc.rightsIn Copyright
dc.subject.otherinverse problems
dc.subject.otherunique continuation
dc.subject.otherfractional Laplacian
dc.subject.otherfractional Schrödinger equation
dc.subject.otherfractional Poincaré inequality
dc.subject.otherRadon transform.
dc.titleUnique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202110285434
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMathematicsen
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange641-681
dc.relation.issn1930-8337
dc.relation.numberinseries4
dc.relation.volume15
dc.type.versionacceptedVersion
dc.rights.copyright© American Institute of Mathematical Sciences (AIMS), 2021
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber284715 HY
dc.relation.grantnumber309963
dc.relation.grantnumber770924
dc.relation.grantnumber770924
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysokvanttimekaniikka
dc.subject.ysoinversio-ongelmat
dc.subject.ysoepäyhtälöt
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p12392
jyx.subject.urihttp://www.yso.fi/onto/yso/p5563
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
jyx.subject.urihttp://www.yso.fi/onto/yso/p15720
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.3934/ipi.2021009
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
dc.relation.funderEuropean Commissionen
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramERC Consolidator Grantfi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramERC Consolidator Granten
jyx.fundinginformationG.C. was partially supported by the European Research Council under Horizon 2020 (ERC CoG 770924). K.M. and J.R. were partially supported by Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963).


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