Determining conductivity with special anisotropy by boundary measurements

We prove results of uniqueness and stability at the boundary for the inverse problem of electrical impedance tomography in the presence of possibly anisotropic conductivities. We assume that the unknown conductivity has the form A = A(x, a(x)), where a(x) is an unknown scalar function and A(x, t) is a given matrix-valued function. We also deduce results of uniqueness in the interior among conductivities A obtained by piecewise analytic perturbations of the scalar term a.