  We prove uniqueness in the inverse conductivity problem for uniformly
elliptic conductivities in $W^{s,p}(\Omega)$, where $\Omega \subset \mathbb
R^n$ is Lipschitz, $3\leq n \leq 6$, and $s$ and $p$ are such that $
W^{s,p}(\Omega)\not \subset W^{1,\infty}(\Omega)$. In particular, we obtain
uniqueness for conductivities in $W^{1,n}(\Omega)$ ($n=3,4$). This improves on
the result of the author and Tataru, who assumed that the conductivity is
Lipschitz.
