Calculus of Variations and Partial Differential Equations· 2026Q1
The global inverse fractional conductivity problem
- 2citations
- Q1SCImago
- 2026year
Short summary
This paper proves uniqueness for an inverse problem involving the fractional conductivity equation, showing that partial Dirichlet-to-Neumann maps in nondisjoint exterior subsets can uniquely determine conductivity.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proves uniqueness for an inverse problem of the fractional conductivity equation.
- Uses partial Dirichlet-to-Neumann (DN) maps measured in nondisjoint exterior subsets.
- Introduces a novel nonlocal exterior determination method.
- Demonstrates exterior determination is independent of unique continuation properties.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Calculus of Variations and Partial Differential Equations, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics