{"paper":{"title":"Conformal mapping for cavity inverse problem: an explicit reconstruction formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandre Munnier, Karim Ramdani","submitted_at":"2015-09-09T09:38:58Z","abstract_excerpt":"In this paper, we address a classical case of the Calder\\'on (or conductivity) inverse problem in dimension two. We aim to recover the location and the shape of a single cavity $\\omega$ (with boundary $\\gamma$) contained in a domain $\\Omega$ (with boundary $\\Gamma$) from the knowledge of the Dirichlet-to-Neumann (DtN) map $\\Lambda_\\gamma: f \\longmapsto \\partial_n u^f|_{\\Gamma}$, where $u^f$ is harmonic in $\\Omega\\setminus\\overline{\\omega}$, $u^f|_{\\Gamma}=f$ and $u^f|_{\\gamma}=c^f$, $c^f$ being the constant such that $\\int_{\\gamma}\\partial_n u^f\\,{\\rm d}s=0$. We obtain an explicit formula for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02693","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}