Inverse Spectral Problem With Low Regularity Refractive Index
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912828051423232 |
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| author | Bu, Kewen Deng, Youjun Jiang, Yan Zhang, Kai |
| author_facet | Bu, Kewen Deng, Youjun Jiang, Yan Zhang, Kai |
| contents | This article investigates the unique determination of a radial refractive index n from spectral data. First, we demonstrate that for piecewise twice continuously differentiable functions, n is not uniquely determined by the special transmission eigenvalues associated with radially symmetric eigenfunctions. Subsequently we prove that if n \in M is twice continuously differentiable functions(or continuously differentiable functions with Lipschitz continuous derivative), then n is uniquely determined on [0,1] by all special transmission eigenvalues when supplemented by partial a priori information on the refractive index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11146 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inverse Spectral Problem With Low Regularity Refractive Index Bu, Kewen Deng, Youjun Jiang, Yan Zhang, Kai Analysis of PDEs 35P20, 35J25, 35R30, 35J05, 35P25 This article investigates the unique determination of a radial refractive index n from spectral data. First, we demonstrate that for piecewise twice continuously differentiable functions, n is not uniquely determined by the special transmission eigenvalues associated with radially symmetric eigenfunctions. Subsequently we prove that if n \in M is twice continuously differentiable functions(or continuously differentiable functions with Lipschitz continuous derivative), then n is uniquely determined on [0,1] by all special transmission eigenvalues when supplemented by partial a priori information on the refractive index. |
| title | Inverse Spectral Problem With Low Regularity Refractive Index |
| topic | Analysis of PDEs 35P20, 35J25, 35R30, 35J05, 35P25 |
| url | https://arxiv.org/abs/2601.11146 |