Reconstruction from boundary measurements for less regular conductivities

Abstract

In this paper, following Nachman's idea and Haberman and Tataru's idea, we reconstruct $C^1$ conductivity $γ$ or Lipchitz conductivity $γ$ with small enough value of $|\nabla logγ|$ in a Lipschitz domain $Ω$ from the Dirichlet-to-Neumann map $Λ_γ$. 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 $Λ_γ$.

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