Monotonicity and Enclosure Methods for the p-Laplace Equation

Abstract

We show that the convex hull of a monotone perturbation of a homogeneous background conductivity in the p-conductivity equation is determined by knowledge of the nonlinear Dirichlet--Neumann operator. We give two independent proofs: one is based on the monotonicity method and the other on the enclosure method. Our results are constructive and require no jump or smoothness properties on the conductivity perturbation or its support.