Superconductive and insulating inclusions for linear and non-linear conductivity equations
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. doi:10.3934/ipi.2018004
Published inInverse Problems and Imaging
© 2018 American Institute of Mathematical Sciences.
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 < ∞.