Anisotropic inverse problems in two dimensions

Let g be a Riemannian metric on a bounded domain in two dimensions with a Lipschitz boundary. We show that one can determine the equivalent class of g and beta in the W-1,W-p topology, p > 2, from knowledge of the associated Dirichletto-Neumann (DN) map Lambda(g,beta) to the elliptic equation div (g)(betadel(g)u) = 0. The DN map encodes all the voltage and current measurements at the boundary.