The Calderón Problem for Quasilinear Conductivities of Conformally Transversally Anisotropic Media

Abstract

This paper investigates Calderón's problem on a conformally transversally anisotropic manifold $(M,g)$ of dimension $n\ge 3$, where the conductivity $a(s,x,p)$ might depend on both the electric potential and the electric field. We establish that for all $(t,x)\in \mathbb{R}\times M$ and $\beta \in {\mathbb{N}}^{1+n}$ the derivatives ${\partial }_{(s,p)}^{\beta }a(s,x,p){|}_{(s,p)=(t,0)}$ are uniquely determined by the boundary voltage-current measurements. If $a(s,x,p)$ is analytic in $p$, then $a(s,x,p)$ can be uniquely recovered.