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We detect an inclusion with infinite conductivity from boundary measurementsrepresented by the Dirichlet-to-Neumann map for the conductivity equation. Weuse both the enclosure method and the probe method. We use the enclosure methodto prove partial results when the underlying equation is the quasilinear$p$-Laplace equation. Further, we rigorously treat the forward problem for thepartial differential equation $\operatorname{div}(\sigma\lvert\nablau\rvert^{p-2}\nabla u)=0$ where the measurable conductivity$\sigma\colon\Omega\to[0,\infty]$ is zero or infinity in large sets and$1<p<\infty$.

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