Reconstruction for the Calderón problem with Lipschitz conductivities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915415032070144 |
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| author | Caro, Pedro García-Ferrero, María Ángeles Rogers, Keith M. |
| author_facet | Caro, Pedro García-Ferrero, María Ángeles Rogers, Keith M. |
| contents | We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz continuous. To determine the conductivity we first solve an associated integral equation locally, finding solutions in $H^1(B)$, where $B$ is a ball that properly contains the body. A key ingredient is to equip this Sobolev space with an equivalent norm which depends on two auxiliary parameters that can be chosen to yield a contraction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reconstruction for the Calderón problem with Lipschitz conductivities Caro, Pedro García-Ferrero, María Ángeles Rogers, Keith M. Analysis of PDEs Classical Analysis and ODEs 35R30 We determine the conductivity of the interior of a body using electrical measurements on its surface. We assume only that the conductivity is bounded below by a positive constant and that the conductivity and surface are Lipschitz continuous. To determine the conductivity we first solve an associated integral equation locally, finding solutions in $H^1(B)$, where $B$ is a ball that properly contains the body. A key ingredient is to equip this Sobolev space with an equivalent norm which depends on two auxiliary parameters that can be chosen to yield a contraction. |
| title | Reconstruction for the Calderón problem with Lipschitz conductivities |
| topic | Analysis of PDEs Classical Analysis and ODEs 35R30 |
| url | https://arxiv.org/abs/2401.06120 |