{"paper":{"title":"Existence, uniqueness and characterisation of local minimisers in higher order Calculus of Variations in $\\mathrm L^{\\infty}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis, Roger Moser","submitted_at":"2024-03-19T10:52:12Z","abstract_excerpt":"We study variational problems for second order supremal functionals $\\mathrm F_\\infty(u)= \\|F(\\cdot,u,\\mathrm D u,\\mathrm{A}\\!:\\!\\mathrm D^2u)\\|_{\\mathrm L^{\\infty}(\\Omega)}$, where $F$ satisfies certain natural assumptions, $\\mathrm A$ is a positive matrix, and $\\Omega \\Subset \\mathbb R^n$. Higher order problems are very novel in the Calculus of Variations in $\\mathrm L^{\\infty}$, and exhibit a strikingly different behaviour compared to first order problems, for which there exists an established theory, pioneered by Aronsson in 1960s. The aim of this paper is to develop a complete theory for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.12625","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.12625/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}