Uniqueness in Calderón’s problem with Lipschitz conductivities

We use Xs,b-inspired spaces to prove a uniqueness result for Calderón’s problem in a Lipschitz domain Ω under the assumption that the conductivity lies in the space W1,∞(Ω‾). For Lipschitz conductivities, we obtain uniqueness for conductivities close to the identity in a suitable sense. We also prove uniqueness for arbitrary C1 conductivities.