Superconductive and insulating inclusions for linear and non-linear conductivity equations
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
also prove similar 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 < ∞.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
American Institute of Mathematical Sciences
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201812175155Use this for linking
Review status
Peer reviewed
ISSN
1930-8337
DOI
https://doi.org/10.3934/ipi.2018004
Language
English
Published in
Inverse Problems and Imaging
Citation
- Brander, T., Ilmavirta, J., & Kar, M. (2018). Superconductive and insulating inclusions for linear and non-linear conductivity equations. Inverse Problems and Imaging, 12(1), 91-123. https://doi.org/10.3934/ipi.2018004
License
Copyright© 2018 American Institute of Mathematical Sciences.