  We investigate a generalization of Calder\'on's problem of recovering the
conductivity coefficient in a conductivity equation from boundary measurements.
  As a model equation we consider the p-conductivity equation with p strictly
between one and infinity, which reduces to the standard conductivity equation
when p equals two, and to the p-Laplace equation when the conductivity is
constant.
  The thesis consists of results on the direct problem, boundary determination
and detecting inclusions. We formulate the equation as a variational problem
also when the conductivity may be zero or infinity in large sets. As a boundary
determination result we recover the first order derivative of a smooth
conductivity on the boundary. We use the enclosure method of Ikehata to recover
the convex hull of an inclusion of finite conductivity and find an upper bound
for the convex hull if the conductivity within an inclusion is zero or
infinite.
