{"paper":{"title":"A Pointwise Characterisation of the PDE System of Vectorial Calculus of Variations in $L^\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Birzhan Ayanbayev (Reading, Nikos Katzourakis (Reading, UK)","submitted_at":"2016-11-18T00:45:24Z","abstract_excerpt":"Let $n,N\\in \\mathbb{N}$ with $\\Omega \\subseteq \\mathbb{R}^n$ open. Given $H \\in C^2(\\Omega \\times \\mathbb{R}^N\\times \\mathbb{R}^{Nn}),$ we consider the functional \\[ \\tag{1} \\label{1}\n  E_\\infty (u,\\mathcal{O})\\, :=\\, \\underset{\\mathcal{O}}{\\mathrm{ess}\\,\\sup}\\, H (\\cdot,u,\\mathrm{D} u) ,\\ \\ \\ u\\in W^{1,\\infty}_\\text{loc}(\\Omega,\\mathbb{R}^N),\\ \\ \\ \\mathcal{O} \\Subset \\Omega. \\] The associated PDE system which plays the role of Euler-Lagrange equations in $L^\\infty$ is \\[ \\label{2} \\tag{2} \\left\\{ \\begin{array}{r} H_{P}(\\cdot, u, \\mathrm{D}u)\\, \\mathrm{D} \\big(H(\\cdot, u, \\mathrm{D} u)\\big) \\,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.05936","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"}