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 bound-ed 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
Fields of Study & Subjects
Numerical methods in inverse problems
Advanced Mathematical Modeling in Engineering
Composite Material Mechanics
Publication details
- Journal / source
- Inverse Problems and Imaging
- Volume
- 27
- Issue
- 0
- Pages
- 208–232
- Publication date
- 11 May 2026
- Language
- EN