{"paper":{"title":"Uniqueness of minimizers of weighted least gradient problems arising in conductivity imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adrian Nachman, Alexandru Tamasan, Amir Moradifam","submitted_at":"2014-04-23T21:39:46Z","abstract_excerpt":"We prove uniqueness for minimizers of the weighted least gradient problem \\[\\inf \\left\\lbrace \\int_{\\Omega} a|Du|: \\ \\ u\\in BV(\\Omega), \\ \\ u|_{\\partial \\Omega}=f \\right\\rbrace.\\] The weight function $a$ is assumed to be continuous and it is allowed to vanish in certain subsets of $\\Omega$. Existence is assumed a priori. Our approach is motivated by the hybrid inverse problem of imaging electric conductivity from interior knowledge (obtainable by MRI) of the magnitude of one current density vector field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5992","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"}