Inverse problems for p-Laplace type equations under monotonicity assumptions

Abstract

We consider inverse problems for p-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying σ1 ≥ σ2 and having the same nonlinear Dirichlet-to-Neumann map must be identical. The proof is based on a monotonicity inequality and the unique continuation principle for p-Laplace type equations. In higher dimensions, where unique continuation is not known, we obtain a similar result for conductivities close to constant.