A uniqueness theorem for inverse problems in quasilinear anisotropic media II

Abstract

We study the question of whether one can uniquely determine scalar quasilinear conductivity in an anisotropic medium by making voltage and current measurements at the boundary. We prove a global uniqueness in the $ C^{2,\alpha} $ category, by showing that the $ C^{2,\alpha} $ quasilinear conductivity in an anisotropic medium can be uniquely determined by the voltage and current measurements at the boundary, i.e., by the Dirichlet to Neumann map, assuming that an anisotropic linear conductivity can be identified by its Dirichlet to Neumann map up to a diffeomorphism that fixes the boundary.