Reconstruction of Rough Conductivities from Boundary Measurements
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911671213096960 |
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| author | Tarikere, Ashwin |
| author_facet | Tarikere, Ashwin |
| contents | We show the validity of Nachman's procedure (Ann. Math. 128(3):531-576, 1988) for reconstructing a conductivity function $γ$ in a smooth bounded domain $Ω\subset \mathbb{R}^n$ ($n\geq 3$) from its Dirichlet-to-Neumann map $Λ_γ$ for less regular conductivities, specifically $γ\in H^{3/2,2n}(Ω)$ such that $γ\equiv 1$ near $\partial Ω$. We also obtain a log-type stability estimate for the inverse problem when $γ$ has slightly higher regularity, i.e., $γ\in H^{2-s,n/s}(Ω)$ for $0 < s <1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_05155 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Reconstruction of Rough Conductivities from Boundary Measurements Tarikere, Ashwin Analysis of PDEs 35R30 We show the validity of Nachman's procedure (Ann. Math. 128(3):531-576, 1988) for reconstructing a conductivity function $γ$ in a smooth bounded domain $Ω\subset \mathbb{R}^n$ ($n\geq 3$) from its Dirichlet-to-Neumann map $Λ_γ$ for less regular conductivities, specifically $γ\in H^{3/2,2n}(Ω)$ such that $γ\equiv 1$ near $\partial Ω$. We also obtain a log-type stability estimate for the inverse problem when $γ$ has slightly higher regularity, i.e., $γ\in H^{2-s,n/s}(Ω)$ for $0 < s <1/2$. |
| title | Reconstruction of Rough Conductivities from Boundary Measurements |
| topic | Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2001.05155 |