Mathematical Review of MR2484149 'Complex geometrical optics solutions for anisotropic equations and applications.' by Takuwa, H.; Uhlmann, G.; Wang, J.-N. , J. Inverse Ill-Posed Probl. 16 (2008), no. 8, 791–804

Let $\Omega$ be a an open, bounded sobset of $\bbd R ^2$ with smooth boundary and $D \subset\Omega$ an open subset such that $\Omega - \bar D$ is connected. Let the background conductivity be a symmetric, positive definite matrix and $u$ solve the conductivity equation in $\Omega$ plus suitable boundary conditions.