{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/boundary-determination-for-hybrid-imaging","title":"Boundary determination for hybrid imaging from a single measurement","arxiv_id":"1904.00644","date":"2019-04-01","proceeding":null,"authors":["Tommi Brander","Torbjørn Ringholm"],"abstract":"We recover the conductivity $\\sigma$ at the boundary of a domain from a combination of interior and boundary data, with a single quite arbitrary measurement, in AET or CDII. The argument is elementary and local. More generally, we consider the variable exponent $p(\\cdot)$-Laplacian as a forward model with the interior data $\\sigma |\\nabla u|^q$, and find out that single measurement specifies the boundary conductivity when $p-q \\ge 1$, and otherwise the measurement specifies two alternatives. We present heuristics for selecting between these alternatives. Both $p$ and $q$ may depend on the spatial variable $x$, but they are assumed to be a priori known. We illustrate the practical situations with numerical examples.","url_abs":"https://arxiv.org/abs/1904.00644v1","url_pdf":"https://arxiv.org/pdf/1904.00644v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"boundary-determination-for-hybrid-imaging","repo_url":"https://github.com/tringholm/bdry-data-calderon","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}