A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910964600799232 |
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| author | Donlon, Niall Gaburro, Romina |
| author_facet | Donlon, Niall Gaburro, Romina |
| contents | We consider the inverse boundary value problem of the simultaneous determination of the coefficients $σ$ and $q$ of the equation $-\mbox{div}(σ\nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion $Σ$ of the boundary $\partial Ω$ of a domain $Ω\subset \mathbb{R}^n$, with $n\geq 3$. We assume that $σ$ and $q$ are \textit{a-priori} known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of $Ω$ with curved interfaces. We prove that $σ$ and $q$ can be uniquely determined in $Ω$ from the knowledge of the local map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18063 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements Donlon, Niall Gaburro, Romina Analysis of PDEs 35R30, 35J10, 35J25 We consider the inverse boundary value problem of the simultaneous determination of the coefficients $σ$ and $q$ of the equation $-\mbox{div}(σ\nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion $Σ$ of the boundary $\partial Ω$ of a domain $Ω\subset \mathbb{R}^n$, with $n\geq 3$. We assume that $σ$ and $q$ are \textit{a-priori} known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of $Ω$ with curved interfaces. We prove that $σ$ and $q$ can be uniquely determined in $Ω$ from the knowledge of the local map. |
| title | A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements |
| topic | Analysis of PDEs 35R30, 35J10, 35J25 |
| url | https://arxiv.org/abs/2505.18063 |