The Calderón Problem for Quasilinear Conductivities of Conformally Transversally Anisotropic Media
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918203176779776 |
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| author | Chen, Xi Jin, Ziyun |
| author_facet | Chen, Xi Jin, Ziyun |
| contents | This paper investigates Calderón's problem on a conformally transversally anisotropic manifold $ (M,g) $ of dimension $n \geq 3$, where the conductivity $ a(s,x,p) $ might depend on both the electric potential and the electric field. We establish that for all $(t,x)\in \mathbb{R}\times M$ and $β\in \mathbb{N}^{1+n}$ the derivatives $ \partial_{(s,p)}^βa(s,x,p)|_{(s,p)=(t,0)}$ are uniquely determined by the boundary voltage-current measurements. If $ a(s,x,p) $ is analytic in $ p $, then $ a(s,x,p) $ can be uniquely recovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Calderón Problem for Quasilinear Conductivities of Conformally Transversally Anisotropic Media Chen, Xi Jin, Ziyun Analysis of PDEs This paper investigates Calderón's problem on a conformally transversally anisotropic manifold $ (M,g) $ of dimension $n \geq 3$, where the conductivity $ a(s,x,p) $ might depend on both the electric potential and the electric field. We establish that for all $(t,x)\in \mathbb{R}\times M$ and $β\in \mathbb{N}^{1+n}$ the derivatives $ \partial_{(s,p)}^βa(s,x,p)|_{(s,p)=(t,0)}$ are uniquely determined by the boundary voltage-current measurements. If $ a(s,x,p) $ is analytic in $ p $, then $ a(s,x,p) $ can be uniquely recovered. |
| title | The Calderón Problem for Quasilinear Conductivities of Conformally Transversally Anisotropic Media |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.12096 |