{"paper":{"title":"Nachman's reconstruction for the Calderon problem with discontinuous conductivities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"George Lytle, Peter Perry, Samuli Siltanen","submitted_at":"2018-09-25T00:52:36Z","abstract_excerpt":"We show that Nachman's integral equations for the Calder\\'on problem, derived for conductivities in $W^{2,p}(\\Omega)$, still hold for $L^\\infty$ conductivities which are $1$ in a neighborhood of the boundary. We also prove convergence of scattering transforms for smooth approximations to the scattering transform of $L^\\infty$ conductivities. We rely on Astala-P\\\"aiv\\\"arinta's formulation of the Calder\\'on problem for a framework in which these convergence results make sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09272","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"}