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Reconstruction for
the Calderón problem with Lipschitz conductivities
Pedro Caro, María Ángeles García-Ferrero and Keith M. Rogers |
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Vol. 18 (2025), No. 8, 2033–2060
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Abstract |
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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 in a ball that properly contains the body, finding solutions in . 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. |
Keywords
Calderón inverse problem, conductivity, reconstruction, low
regularity
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Mathematical Subject Classification
Primary: 35R30
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Milestones
Received: 17 January 2024
Revised: 5 July 2024
Accepted: 20 September 2024
Published: 25 July 2025
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Authors |
| Pedro Caro | |
| Basque Center for Applied
Mathematics Bilbao Spain |
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| María Ángeles García-Ferrero | |
| Instituto de Ciencias
Matemáticas CSIC-UAM-UC3M-UCM Madrid Spain |
Universitat de Barcelona Barcelona Spain |
| Keith M. Rogers | |
| Instituto de Ciencias
Matemáticas CSIC-UAM-UC3M-UCM Madrid Spain |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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