dc.contributor.author Brander, Tommi dc.date.accessioned 2016-03-23T10:54:56Z dc.date.available 2016-03-23T10:54:56Z dc.date.issued 2016 dc.identifier.isbn 978-951-39-6576-1 dc.identifier.other oai:jykdok.linneanet.fi:1524683 dc.identifier.uri https://jyx.jyu.fi/handle/123456789/49173 dc.description.abstract We 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.extent Verkkoaineisto (17 sivua ja 35 numeroimatonta sivua) dc.language.iso eng dc.publisher University of Jyväskylä dc.relation.ispartofseries Report / University of Jyväskylä. Department of Mathematics and Statistics dc.relation.haspart Article I: Brander, T., Kar, M., & Salo, M. (2015). Enclosure method for the p-Laplace equation. Inverse Problems, 31(4), 045001. DOI: 10.1088/0266-5611/31/4/045001 dc.relation.haspart Article II: Brander, T. (2016). Calderón problem for the 𝑝-Laplacian: First order derivative of conductivity on the boundary. Proceedings of the American Mathematical Society, 144(1), 177-189. DOI: 10.1090/proc/12681 dc.relation.haspart Article III: Brander, T., Ilmavirta, J., & Kar, M. Superconductive and insulating inclusions for non-linear conductivity equations. Preprint. dc.relation.isversionof Julkaistu myös painettuna (Yhteenveto-osa ja 3 eripainosta). dc.subject.other reunamääritys dc.subject.other kotelointimenetelmä dc.subject.other inverse problem dc.subject.other Calderón's problem dc.subject.other electrical impedance tomography dc.subject.other p-Laplace equation dc.title Calderón's problem for p-laplace type equations dc.type Diss. fi dc.identifier.urn URN:ISBN:978-951-39-6576-1 dc.type.dcmitype Text en dc.type.ontasot Väitöskirja fi dc.type.ontasot Doctoral dissertation en dc.contributor.tiedekunta Matemaattis-luonnontieteellinen tiedekunta fi dc.contributor.yliopisto University of Jyväskylä en dc.contributor.yliopisto Jyväskylän yliopisto fi dc.contributor.oppiaine Matematiikka fi dc.relation.issn 1457-8905 dc.relation.numberinseries 155 dc.rights.accesslevel openAccess fi dc.subject.yso inversio-ongelmat dc.subject.yso Calderónin ongelma dc.subject.yso osittaisdifferentiaaliyhtälöt dc.subject.yso p-Laplace -yhtälö dc.subject.yso sähkönjohtavuus dc.subject.yso impedanssitomografia
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