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dc.contributor.authorLassas, Matti
dc.contributor.authorLiimatainen, Tony
dc.contributor.authorSalo, Mikko
dc.date.accessioned2020-11-19T08:33:17Z
dc.date.available2020-11-19T08:33:17Z
dc.date.issued2020
dc.identifier.citationLassas, M., Liimatainen, T., & Salo, M. (2020). The Poisson embedding approach to the Calderón problem. <i>Mathematische Annalen</i>, <i>377</i>(1-2), 19-67. <a href="https://doi.org/10.1007/s00208-019-01818-3" target="_blank">https://doi.org/10.1007/s00208-019-01818-3</a>
dc.identifier.otherCONVID_28964225
dc.identifier.otherTUTKAID_80918
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/72680
dc.description.abstractWe introduce a new approach to the anisotropic Calderón problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calderón type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result of Lassas et al. (Annales de l’ ENS 34(5):771–787, 2001) solving the Calderón problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesMathematische Annalen
dc.rightsCC BY 4.0
dc.subject.otherCalderón problem
dc.subject.otherPoisson embedding
dc.titleThe Poisson embedding approach to the Calderón problem
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202011186682
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.date.updated2020-11-18T10:15:06Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange19-67
dc.relation.issn0025-5831
dc.relation.numberinseries1-2
dc.relation.volume377
dc.type.versionpublishedVersion
dc.rights.copyright© The Author(s) 2019
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber284715 HY
dc.relation.grantnumber307023
dc.relation.grantnumber307023
dc.relation.grantnumber309963
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.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/s00208-019-01818-3
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramFP7 (EU's 7th Framework Programme)en
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramERC Consolidator Granten
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramEU:n 7. puiteohjelma (FP7)fi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramERC Consolidator Grantfi
jyx.fundinginformationOpen access funding provided by University of Jyväskylä (JYU). M.L., T.L. and M.S. were supported by the Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963). M.S. was also partly supported by the European Research Council under FP7/2007-2013 (ERC StG 307023) and Horizon 2020 (ERC CoG 770924). We would like to thank an anonymous referee for valuable comments.
dc.type.okmA1


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