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dc.contributor.authorLassas, Matti
dc.contributor.authorLiimatainen, Tony
dc.contributor.authorLin, Yi-Hsuan
dc.contributor.authorSalo, Mikko
dc.date.accessioned2020-12-22T08:40:02Z
dc.date.available2020-12-22T08:40:02Z
dc.date.issued2021
dc.identifier.citationLassas, M., Liimatainen, T., Lin, Y.-H., & Salo, M. (2021). Inverse problems for elliptic equations with power type nonlinearities. <i>Journal de Mathematiques Pures et Appliquees</i>, <i>145</i>, 44-82. <a href="https://doi.org/10.1016/j.matpur.2020.11.006" target="_blank">https://doi.org/10.1016/j.matpur.2020.11.006</a>
dc.identifier.otherCONVID_47043836
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/73381
dc.description.abstractWe introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension 2, and a potential on transversally anisotropic manifolds in dimensions . In the Euclidean case, we show that one can solve the Calderón problem for certain semilinear equations in a surprisingly simple way without using complex geometrical optics solutions.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofseriesJournal de Mathematiques Pures et Appliquees
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherinverse boundary value problem
dc.subject.otherCalderón problem
dc.subject.othersemilinear equation
dc.subject.othertransversally anisotropic
dc.titleInverse problems for elliptic equations with power type nonlinearities
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202012227323
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.description.reviewstatuspeerReviewed
dc.format.pagerange44-82
dc.relation.issn0021-7824
dc.relation.volume145
dc.type.versionacceptedVersion
dc.rights.copyright© 2020 Elsevier
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber309963
dc.relation.grantnumber284715 HY
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-nc-nd/4.0/
dc.relation.doi10.1016/j.matpur.2020.11.006
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundinginformationAll authors were supported by the Finnish Centre of Excellence in Inverse Modelling and Imaging (Academy of Finland grant 284715). M.S. was also supported by the Academy of Finland (grant 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924). Y.-H. L. is partially supported by the Ministry of Science and Technology, Taiwan, under the Columbus Pro-gram:MOST-109-2636-M-009-006, 2020-2025.


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