{"paper":{"title":"Solutions of Vectorial Hamilton-Jacobi Equations are Rank-One Absolute Minimisers in $L^\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis (Reading, UK)","submitted_at":"2016-04-04T10:19:31Z","abstract_excerpt":"Given the supremal functional $E_\\infty(u,\\Omega')=ess\\,\\sup_{\\Omega'} H(\\cdot,D u)$ defined on $W^{1,\\infty}_{loc}(\\Omega,\\mathbb{R}^N)$, $\\Omega' \\Subset \\Omega\\subseteq \\mathbb{R}^n$, we identify a class of vectorial rank-one Absolute Minimisers by proving a statement slightly stronger than the next claim: vectorial solutions of the Hamilton-Jacobi equation $H(\\cdot,D u)=c$ are rank-one Absolute Minimisers if they are $C^1$. Our minimality notion is a generalisation of the classical $L^\\infty$ variational principle of Aronsson to the vector case and emerged in earlier work of the author. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00802","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"}