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dc.contributor.authorBrander, Tommi
dc.date.accessioned2016-03-23T10:54:56Z
dc.date.available2016-03-23T10:54:56Z
dc.date.issued2016
dc.identifier.isbn978-951-39-6576-1
dc.identifier.otheroai:jykdok.linneanet.fi:1524683
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/49173
dc.description.abstractWe investigate a generalization of Calderón’s problem of recovering the conductivity coefficient in a conductivity equation from boundary measurements. As a model equation we consider the p-conductivity equation div σ |∇u|p−2 ∇u = 0 with 1 < p < ∞, which reduces to the standard conductivity equation when p = 2. The thesis consists of results on the direct problem, boundary determination and detecting inclusions. We formulate the equation as a variational problem also when the conductivity σ may be zero or infinity in large sets. As a boundary determination result we recover the first order derivative of a smooth conductivity on the boundary. We use the enclosure method of Ikehata to recover the convex hull of an inclusion of finite conductivity and find an upper bound for the convex hull if the conductivity within an inclusion is zero or infinite.
dc.format.extentVerkkoaineisto (17 sivua ja 35 numeroimatonta sivua)
dc.language.isoeng
dc.publisherUniversity of Jyväskylä
dc.relation.ispartofseriesReport / University of Jyväskylä. Department of Mathematics and Statistics
dc.relation.haspart<b>Article I:</b> Brander, T., Kar, M., & Salo, M. (2015). Enclosure method for the p-Laplace equation. <i>Inverse Problems, 31(4), 045001. </i><a href=" http://dx.doi.org/ 10.1088/0266-5611/31/4/045001 "target="_blank">DOI: 10.1088/0266-5611/31/4/045001 </a>
dc.relation.haspart<b>Article II:</b> Brander, T. (2016). Calderón problem for the 𝑝-Laplacian: First order derivative of conductivity on the boundary. <i>Proceedings of the American Mathematical Society, 144(1), 177-189. </i><a href=" http://dx.doi.org/ 10.1090/proc/12681 "target="_blank">DOI: 10.1090/proc/12681 </a>
dc.relation.haspart<b>Article III:</b> Brander, T., Ilmavirta, J., & Kar, M. Superconductive and insulating inclusions for non-linear conductivity equations. <i>Preprint</i>.
dc.relation.isversionofJulkaistu myös painettuna (Yhteenveto-osa ja 3 eripainosta).
dc.subject.otherreunamääritys
dc.subject.otherkotelointimenetelmä
dc.subject.otherinverse problem
dc.subject.otherCalderón's problem
dc.subject.otherelectrical impedance tomography
dc.subject.otherp-Laplace equation
dc.titleCalderón's problem for p-laplace type equations
dc.typeDiss.fi
dc.identifier.urnURN:ISBN:978-951-39-6576-1
dc.type.dcmitypeTexten
dc.type.ontasotVäitöskirjafi
dc.type.ontasotDoctoral dissertationen
dc.contributor.tiedekuntaMatemaattis-luonnontieteellinen tiedekuntafi
dc.contributor.yliopistoUniversity of Jyväskyläen
dc.contributor.yliopistoJyväskylän yliopistofi
dc.contributor.oppiaineMatematiikkafi
dc.relation.issn1457-8905
dc.relation.numberinseries155
dc.rights.accesslevelopenAccessfi
dc.subject.ysoinversio-ongelmat
dc.subject.ysoCalderónin ongelma
dc.subject.ysoosittaisdifferentiaaliyhtälöt
dc.subject.ysop-Laplace -yhtälö
dc.subject.ysosähkönjohtavuus
dc.subject.ysoimpedanssitomografia


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