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dc.contributor.authorKenig, Carlos
dc.contributor.authorSalo, Mikko
dc.date.accessioned2016-01-27T10:23:38Z
dc.date.available2016-01-27T10:23:38Z
dc.date.issued2013
dc.identifier.citationKenig, C., & Salo, M. (2013). The Calderón problem with partial data on manifolds and applications. <i>Analysis & PDE</i>, <i>6</i>(8), 2003-2048. <a href="https://doi.org/10.2140/apde.2013.6.2003" target="_blank">https://doi.org/10.2140/apde.2013.6.2003</a>
dc.identifier.otherCONVID_23709277
dc.identifier.otherTUTKAID_62057
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/48487
dc.description.abstractWe consider Calderón’s inverse problem with partial data in dimensions n ≥ 3. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility of a broken geodesic ray transform. In Euclidean space, sets satisfying the flatness condition include parts of cylindrical sets, conical sets, and surfaces of revolution. We prove local uniqueness in the Calderón problem with partial data in admissible geometries, and global uniqueness under an additional concavity assumption. This work unifies two earlier approaches to this problem— one by Kenig, Sjöstrand, and Uhlmann, the other by Isakov— and extends both. The proofs are based on improved Carleman estimates with boundary terms, complex geometrical optics solutions involving reflected Gaussian beam quasimodes, and invertibility of (broken) geodesic ray transforms. This last topic raises questions of independent interest in integral geometry.
dc.language.isoeng
dc.publisherMathematical Sciences Publishers
dc.relation.ispartofseriesAnalysis & PDE
dc.subject.othercalderón problem
dc.subject.otherpartial data
dc.subject.otherinverse problem
dc.titleThe Calderón problem with partial data on manifolds and applications
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201601201209
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2016-01-20T16:15:21Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange2003-2048
dc.relation.issn2157-5045
dc.relation.numberinseries8
dc.relation.volume6
dc.type.versionpublishedVersion
dc.rights.copyright© Mathematical Sciences Publishers 2013. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.2140/apde.2013.6.2003


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