We use -inspired spaces to prove a uniqueness result for Calderón’s problem in a Lipschitz domain under the assumption that the conductivity lies in the space . For Lipschitz conductivities, we obtain uniqueness for conductivities close to the identity in a suitable sense. We also prove uniqueness for arbitrary conductivities.
Boaz Haberman. Daniel Tataru. "Uniqueness in Calderón’s problem with Lipschitz conductivities." Duke Math. J. 162 (3) 497 - 516, 15 February 2013. https://doi.org/10.1215/00127094-2019591