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 | <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.isversionof | Julkaistu myös painettuna (Yhteenveto-osa ja 3 eripainosta). | |
dc.rights | In Copyright | |
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. | |
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 | |
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 | |
dc.rights.url | https://rightsstatements.org/page/InC/1.0/ | |