{"paper":{"title":"On Second-Order $L^\\infty$ Variational Problems with Lower-Order Terms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ben Dutton, Nikos Katzourakis","submitted_at":"2024-12-16T12:24:47Z","abstract_excerpt":"In this paper we study $2$nd order $L^\\infty$ variational problems, through seeking to minimise a supremal functional involving the Hessian of admissible functions as well as lower-order terms. Specifically, given a bounded domain $\\Omega\\subseteq \\mathbb R^n$ and $\\mathrm H : \\Omega\\times\\big(\\mathbb R \\times\\mathbb R^n \\times \\mathbb R^{n^{\\otimes2}}_s \\big) \\to \\mathbb R$, we consider the functional \\[ \\mathrm{E}_\\infty(u, \\mathcal{O}) :=\\underset{ \\mathcal{O}}{\\mathrm{ess}\\sup}\\hspace{1mm}\\mathrm H (\\cdot,u,\\mathrm D u,\\mathrm D^2u ) , \\ \\ u\\in W^{2,\\infty}(\\Omega), \\ \\mathcal{O} \\subseteq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11701","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.11701/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"}