Reconstruction of Rough Conductivities from Boundary Measurements

Abstract

We show the validity of Nachman's procedure (Ann. Math. 128(3):531-576, 1988) for reconstructing a conductivity function $\gamma$ in a smooth bounded domain $\Omega \subset \mathbb{R}^n$ ($n\geq 3$) from its Dirichlet-to-Neumann map $\Lambda_\gamma$ for less regular conductivities, specifically $\gamma \in H^{3/2,2n}(\Omega)$ such that $\gamma \equiv 1$ near $\partial \Omega$. We also obtain a log-type stability estimate for the inverse problem when $\gamma$ has slightly higher regularity, i.e., $\gamma \in H^{2-s,n/s}(\Omega)$ for $0 < s <1/2$.