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dc.contributor.authorFerreira, David Dos Santos
dc.contributor.authorKenig, Carlos E.
dc.contributor.authorSalo, Mikko
dc.date.accessioned2018-01-12T11:11:25Z
dc.date.available2018-01-12T11:11:25Z
dc.date.issued2013
dc.identifier.citationFerreira, D. D. S., Kenig, C. E., & Salo, M. (2013). Determining an unbounded potential from Cauchy data in admissible geometries. <i>Communications in Partial Differential Equations</i>, <i>38</i>(1), 50-68. <a href="https://doi.org/10.1080/03605302.2012.736911" target="_blank">https://doi.org/10.1080/03605302.2012.736911</a>
dc.identifier.otherCONVID_23107942
dc.identifier.otherTUTKAID_59878
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/56705
dc.description.abstractIn [4 Dos Santos Ferreira , D. , Kenig , C.E. , Salo , M. , Uhlmann , G. ( 2009 ). Limiting Carleman weights and anisotropic inverse problems . Invent. Math. 178 : 119 – 171 . [Crossref], [Web of Science ®], [Google Scholar] ] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrödinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n ≥ 3. In this article we extend this result to the case of unbounded potentials, namely those in L n/2. In the process, we derive L p Carleman estimates with limiting Carleman weights similar to the Euclidean estimates of Jerison and Kenig [8 Jerison , D. , Kenig , C.E. ( 1985 ). Unique continuation and absence of positive eigenvalues for Schrödinger operators . Ann. Math. 121 : 463 – 494 . [Crossref], [Web of Science ®], [Google Scholar] ] and Kenig et al. [9 Kenig , C.E. , Ruiz , A. , Sogge , C.D. ( 1987 ). Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators . Duke Math. J. 55 : 329 – 347 . [Crossref], [Web of Science ®], [Google Scholar] ].
dc.language.isoeng
dc.publisherTaylor & Francis
dc.relation.ispartofseriesCommunications in Partial Differential Equations
dc.relation.urihttp://dx.doi.org/10.1080/03605302.2012.736911
dc.subject.otherAttenuated geodesic ray transform
dc.subject.otherCalderón inverse problem
dc.subject.otherCarleman estimates
dc.subject.otherComplex geometrical optics
dc.subject.otherSpectral cluster
dc.titleDetermining an unbounded potential from Cauchy data in admissible geometries
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201801121162
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.updated2018-01-12T10:15:06Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange50-68
dc.relation.issn0360-5302
dc.relation.numberinseries1
dc.relation.volume38
dc.type.versionacceptedVersion
dc.rights.copyright© Taylor & Francis Group, LLC, 2013. This is a final draft version of an article whose final and definitive form has been published by Taylor & Francis Group, LLC. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1080/03605302.2012.736911


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