  This paper is inspired by an imaging problem encountered in the framework of
Electrical Resistance Tomography involving two different materials, one or both
of which are nonlinear. Tomography with nonlinear materials is in the early
stages of developments, although breakthroughs are expected in the
not-too-distant future.
  We consider nonlinear constitutive relationships which, at a given point in
the space, present a behaviour for large arguments that is described by
monomials of order p and q.
  The original contribution this work makes is that the nonlinear problem can
be approximated by a weighted p-Laplace problem. From the perspective of
tomography, this is a significant result because it highlights the central role
played by the $p-$Laplacian in inverse problems with nonlinear materials.
Moreover, when p=2, this provides a powerful bridge to bring all the imaging
methods and algorithms developed for linear materials into the arena of
problems with nonlinear materials.
  The main result of this work is that for "large" Dirichlet data in the
presence of two materials of different order (i) one material can be replaced
by either a perfect electric conductor or a perfect electric insulator and (ii)
the other material can be replaced by a material giving rise to a weighted
p-Laplace problem.
