Inverse problems for the Bakry-Émery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913771505582080 |
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| author | Borthwick, Jack Kamran, Niky |
| author_facet | Borthwick, Jack Kamran, Niky |
| contents | We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-Émery Laplacian $-Δ_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary $(\overline{M},g)$, endowed with a volume form $\mathfrak{m}=e^{-V}ω_g$. These consist in recovering the Taylor coefficients of metric $g$ and weight $V$ along the boundary of $\overline{M}$ from the knowledge of a pair of operators that can be viewed as geometrically natural Dirichlet-to-Neumann maps associated to $-Δ_{\mathcal E}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse problems for the Bakry-Émery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness Borthwick, Jack Kamran, Niky Analysis of PDEs We study the questions of uniqueness and non-uniqueness for a pair of closely related inverse problems for the Bakry-Émery Laplacian $-Δ_{\mathcal E}$ on a smooth compact and oriented Riemannian manifold with boundary $(\overline{M},g)$, endowed with a volume form $\mathfrak{m}=e^{-V}ω_g$. These consist in recovering the Taylor coefficients of metric $g$ and weight $V$ along the boundary of $\overline{M}$ from the knowledge of a pair of operators that can be viewed as geometrically natural Dirichlet-to-Neumann maps associated to $-Δ_{\mathcal E}$. |
| title | Inverse problems for the Bakry-Émery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.21944 |