{"paper":{"title":"On the numerical approximation of vectorial absolute minimisers in $L^\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis, Tristan Pryer (Reading, UK)","submitted_at":"2018-12-28T13:43:47Z","abstract_excerpt":"Let $\\Omega$ be an open set. We consider the supremal functional \\[ \\tag{1}\n  \\label{1} \\ \\ \\ \\ \\ \\ \\mathrm{E}_\\infty (u,\\mathcal{O})\\, :=\\, \\| \\mathrm D u \\|_{L^\\infty( \\mathcal{O} )}, \\ \\ \\ \\mathcal{O} \\subseteq \\Omega \\text{ open}, \\] applied to locally Lipschitz mappings $u : \\mathbb R^n \\supseteq \\Omega \\longrightarrow \\mathbb R^N$, where $n,N\\in \\mathbb N$. This is the model functional of Calculus of Variations in $L^\\infty$. The area is developing rapidly, but the vectorial case of $N\\geq 2$ is still poorly understood. Due to the non-local nature of \\eqref{1}, usual minimisers are not t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10988","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"}