Reconstruction from boundary measurements for less regular conductivities

In this paper, following Nachman’s idea and Haberman and Tataru’s idea, we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $\mathrm{\mid }\mathrm{\nabla }log\gamma \mathrm{\mid }$ in a Lipschitz domain $\mathrm{\Omega }$ from the Dirichlet-to-Neumann map ${\mathrm{\Lambda }}_{\gamma }$. In the appendix the authors and R. M. Brown recover the gradient of a $C^1$-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map ${\mathrm{\Lambda }}_{\gamma }$.