The global inverse fractional conductivity problem
Abstract
uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be nontrivial in the exterior of the domain and isotropic, while the data is given in the form of partial Dirichlet-to-Neumann (DN) maps measured in nondisjoint open subsets of the exterior. This can be seen as the fractional counterpart of the classical inverse conductivity problem. The proof is based on a unique continuation property (UCP) for the DN maps and a novel exterior determination method from the partial exterior DN maps, which is a nonlocal analog of the classical boundary determination method by Kohn and Vogelius. Exterior determination is achieved independently of the UCP and despite the nonlocality of the equation.
Fields of Study & Subjects
Numerical methods in inverse problems
Advanced Mathematical Modeling in Engineering
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 65
- Issue
- 9
- Pages
- 258–258
- Publication date
- 1 September 2026
- Language
- EN