Reconstruction of rough conductivities from boundary measurements

We show the validity of Nachman's procedure (Ann. Math. 128(3):531-576, 1988) for reconstructing a conductivity function γ in a smooth bound-ed domain Ω ⊂ Rⁿ (n≥ 3) from its Dirichlet-to-Neumann map Λ_γ for less regular conductivities, specifically γ ∈ H3/2, 2n(Ω) such that γ ≡ 1 near ∂ Ω. We also obtain a log-type stability estimate for the inverse problem when γ has slightly higher regularity, i.e., γ ∈ H2-s, n/s(Ω) for $ 0 < s <1/2 $.