Uniqueness in Calderón’s problem with Lipschitz conductivities

Abstract

We use $X^{s,b}$-inspired spaces to prove a uniqueness result for Calderón’s problem in a Lipschitz domain $\Omega$ under the assumption that the conductivity lies in the space $W^{1,\infty }\left(\bar{\Omega }\right)$. For Lipschitz conductivities, we obtain uniqueness for conductivities close to the identity in a suitable sense. We also prove uniqueness for arbitrary $C^1$ conductivities.