{"paper":{"title":"Existence and uniqueness of minimizers of general least gradient problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Adrian I. Nachman, Amir Moradifam, Robert L. Jerrard","submitted_at":"2013-05-02T18:58:25Z","abstract_excerpt":"Motivated by problems arising in conductivity imaging, we prove existence, uniqueness, and comparison theorems - under certain sharp conditions - for minimizers of the general least gradient problem \\[\\inf_{u\\in BV_f(\\Omega)} \\int_{\\Omega}\\varphi(x,Du),\\] where $f:\\partial \\Omega\\to \\R$ is continuous, \\[ BV_f(\\Omega):=\\{v\\in BV(\\Omega): \\ \\ \\forall x\\in \\partial \\Omega, \\ \\ \\lim_{r\\to 0} \\ \\esssup_{y\\in \\Omega, |x-y|<r} |f(x) - v(y)| = 0 \\ \\} %BV_f(\\Omega)=\\{u\\in BV(\\Omega): {0.1cm} u|_{\\partial \\Omega}=f {0.1cm} \\hbox{and} {0.1cm} {0.1cm} u {0.1cm} \\hbox{is continuous at} {0.1cm} \\partial \\Om"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0535","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"}