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dc.contributor.authorFerreira, David Dos Santos
dc.contributor.authorKurylev, Yaroslav
dc.contributor.authorLassas, Matti
dc.contributor.authorSalo, Mikko
dc.date.accessioned2016-11-21T11:48:03Z
dc.date.available2016-11-21T11:48:03Z
dc.date.issued2016
dc.identifier.citationFerreira, D. D. S., Kurylev, Y., Lassas, M., & Salo, M. (2016). The Calderón problem in transversally anisotropic geometries. <i>Journal of the European Mathematical Society</i>, <i>18</i>(11), 2579-2626. <a href="https://doi.org/10.4171/JEMS/649" target="_blank">https://doi.org/10.4171/JEMS/649</a>
dc.identifier.otherCONVID_26273530
dc.identifier.otherTUTKAID_71493
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/51940
dc.description.abstractWe consider the anisotropic Calder´on problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work [13], it was shown that a metric in a fixed conformal class is uniquely determined by boundary measurements under two conditions: (1) the metric is conformally transversally anisotropic (CTA), and (2) the transversal manifold is simple. In this paper we will consider geometries satisfying (1) but not (2). The first main result states that the boundary measurements uniquely determine a mixed Fourier transform / attenuated geodesic ray transform (or integral against a more general semiclassical limit measure) of an unknown coefficient. In particular, one obtains uniqueness results whenever the geodesic ray transform on the transversal manifold is injective. The second result shows that the boundary measurements in an infinite cylinder uniquely determine the transversal metric. The first result is proved by using complex geometrical optics solutions involving Gaussian beam quasimodes, and the second result follows from a connection between the Calder´on problem and Gel’fand’s inverse problem for the wave equation and the boundary control method.
dc.language.isoeng
dc.publisherEuropean Mathematical Society Publishing House; European Mathematical Society
dc.relation.ispartofseriesJournal of the European Mathematical Society
dc.subject.otherinverse boundary value problem
dc.subject.otherCalderón problem
dc.subject.otherRiemannian manifold
dc.subject.othercomplex geometrical optics solution
dc.subject.otherboundary control method
dc.titleThe Calderón problem in transversally anisotropic geometries
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201611184673
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.updated2016-11-18T13:15:28Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange2579-2626
dc.relation.issn1435-9855
dc.relation.numberinseries11
dc.relation.volume18
dc.type.versionacceptedVersion
dc.rights.copyright© 2016 EMS Publishing House. This is a final draft version of an article whose final and definitive form has been published by EMS Publishing House. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.4171/JEMS/649


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