The local Calderón problem and the determination at the boundary of a complex anisotropic admittivity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910177308966912 |
|---|---|
| author | Crosse, Jessica Gaburro, Romina |
| author_facet | Crosse, Jessica Gaburro, Romina |
| contents | We address Calderón's problem of stably determining the anisotropic complex admittivity $σ$ in a domain $Ω\subset\mathbb{R}^n$, with $n\geq3$, representing a conducting medium, in terms of a Dirichlet-to-Neumann map locally prescribed on a non-empty portion $Σ$ of the boundary of $Ω$, $\partialΩ$. $σ$ is assumed to be of type $σ(\cdot)=A(\cdot,a(\cdot))$ in $Ω$, where the one-parameter family of complex-symmetric matrices $[λ^{-1},\:λ]\ni t\mapsto A(\cdot,\: t)$ is assumed to be a-priori known and the scalar function $a$ is unknown. We establish Lipschitz and Hölder stability estimates at the boundary for $σ$ and its derivatives of arbitrary order on $Σ$, respectively, in terms of the local map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The local Calderón problem and the determination at the boundary of a complex anisotropic admittivity Crosse, Jessica Gaburro, Romina Analysis of PDEs We address Calderón's problem of stably determining the anisotropic complex admittivity $σ$ in a domain $Ω\subset\mathbb{R}^n$, with $n\geq3$, representing a conducting medium, in terms of a Dirichlet-to-Neumann map locally prescribed on a non-empty portion $Σ$ of the boundary of $Ω$, $\partialΩ$. $σ$ is assumed to be of type $σ(\cdot)=A(\cdot,a(\cdot))$ in $Ω$, where the one-parameter family of complex-symmetric matrices $[λ^{-1},\:λ]\ni t\mapsto A(\cdot,\: t)$ is assumed to be a-priori known and the scalar function $a$ is unknown. We establish Lipschitz and Hölder stability estimates at the boundary for $σ$ and its derivatives of arbitrary order on $Σ$, respectively, in terms of the local map. |
| title | The local Calderón problem and the determination at the boundary of a complex anisotropic admittivity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.26458 |