{"paper":{"title":"Existence of 1D vectorial Absolute Minimisers in $L^\\infty$ under minimal assumptions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hussien Abugirda (Reading, Nikos Katzourakis (Reading, UK)","submitted_at":"2016-04-11T18:59:36Z","abstract_excerpt":"We prove the existence of vectorial Absolute Minimisers in the sense of Aronsson to the supremal functional $E_\\infty(u,\\Omega') = \\|\\mathscr{L}(\\cdot,u,D u)\\|_{L^\\infty(\\Omega')}$, $\\Omega'\\Subset \\Omega$, applied to $W^{1,\\infty}$ maps $u:\\Omega\\subseteq \\mathbb{R}\\longrightarrow \\mathbb{R}^N$ with given boundary values. The assumptions on $\\mathscr{L}($ are minimal, improving earlier existence results previously established by Barron-Jensen-Wang and by the second author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03068","kind":"arxiv","version":3},"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"}