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 $\Omega \subset {\mathbb{R}}^n$ ($n\ge 3$) 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 $0<s<1/2$.

References in corpus (1)

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