  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 $\operatorname{div}(\sigma\lvert\nabla
u\rvert^{p-2}\nabla u)=0$ where the measurable conductivity
$\sigma\colon\Omega\to[0,\infty]$ is zero or infinity in large sets and
$1<p<\infty$.
