Superconductive and insulating inclusions for linear and non-linear conductivity equations

Tommi Olavi Brander, Joonas Ilmavirta, Manas Kar

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We detect an inclusion with infinite conductivity from boundary measurements represented by the Dirichlet-to-Neumann map for the conductivity equation. We use both the enclosure method and the probe method. We use the enclosure method to prove partial results when the underlying equation is the quasilinear p-Laplace equation. Further, we rigorously treat the forward problem for the partial differential equation div(σ|∇u| p−2∇u) = 0 where the measurable conductivity σ : Ω → [0, ∞] is zero or infinity in large sets and 1 < p < ∞.
Original languageEnglish
JournalInverse Problems and Imaging
Volume12
Issue number1
Pages (from-to)91-123
ISSN1930-8337
DOIs
Publication statusPublished - 2018
Externally publishedYes

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