Reconstruction for the Calderón problem with Lipschitz conductivities
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 associate...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/425190 |
| Acceso en línea: | http://hdl.handle.net/10261/425190 https://www.scopus.com/inward/record.uri?eid=2-s2.0-105013988688&doi=10.2140%2Fapde.2025.18.2033&partnerID=40&md5=3c7ade27171dd40f67ba2f4acb2121c5 |
| Access Level: | acceso abierto |
| Palabra clave: | Calderón inverse problem conductivity low regularity reconstruction |
| Sumario: | 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 B that properly contains the body, finding solutions in H1(B). 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. © 2025 The Authors, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open. |
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