Uniqueness in Calderón’s Problem for Conductivities with Unbounded Gradient

Abstract

We prove uniqueness in the inverse conductivity problem for uniformly elliptic conductivities in (Formula presented.), where (Formula presented.) is Lipschitz, (Formula presented.), and s and p are such that (Formula presented.),(Formula presented.). In particular, we obtain uniqueness for conductivities in (Formula presented.). This improves on the result of the author and Tataru, who assumed that the conductivity is Lipschitz.