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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.10408 |
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Table of Contents:
- We extend monotonicity-based inversion methods to an inverse coefficient problem for the isotropic nonlocal elliptic equation \[ (-\nabla \cdot σ\nabla)^s u = 0 \quad \text{in } Ω\subset \mathbb{R}^n, \] where $0 < s < 1$, $n \geq 3$, and $Ω$ is a bounded open set. We establish a monotonicity relation between the leading coefficient $σ$ and the (partial) exterior Dirichlet-to-Neumann (DN) map. Our main result shows that a monotonicity ordering of the coefficients implies a corresponding ordering of the DN maps. Furthermore, we construct localized potentials for the nonlocal equation, which yield a local uniqueness result for the fractional inverse problem.