{"paper":{"title":"A local estimate for vectorial total variation minimization in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Giacomelli, Micha{\\l} {\\L}asica","submitted_at":"2018-06-06T23:15:10Z","abstract_excerpt":"Let $\\boldsymbol u$ be the minimizer of vectorial total variation ($VTV$) with $L^2$ data-fidelity term on an interval $I$. We show that the total variation of $\\boldsymbol u$ over any subinterval of $I$ is bounded by that of the datum over the same subinterval. We deduce analogous statement for the vectorial total variation flow on $I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02456","kind":"arxiv","version":2},"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"}