{"paper":{"title":"Existence, Uniqueness and Structure of Second Order absolute minimisers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis (Reading, Roger Moser (Bath, UK)","submitted_at":"2017-01-12T14:27:04Z","abstract_excerpt":"Let $\\Omega \\subseteq \\mathbb{R}^n$ be a bounded open $C^{1,1}$ set. In this paper we prove the existence of a unique second order absolute minimiser $u_\\infty$ of the functional \\[ \\mathrm{E}_\\infty (u,\\mathcal{O})\\, :=\\, \\| \\mathrm{F}(\\cdot, \\Delta u) \\|_{L^\\infty( \\mathcal{O} )}, \\ \\ \\ \\mathcal{O} \\subseteq \\Omega \\text{ measurable}, \\] with prescribed boundary conditions for $u$ and $\\mathrm{D} u$ on $\\partial \\Omega$ and under natural assumptions on $\\mathrm{F}$. We also show that $u_\\infty$ is partially smooth and there exists a harmonic function $f_\\infty \\in L^1(\\Omega)$ such that \\[ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03348","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"}