{"paper":{"title":"Second Order $L^\\infty$ Variational Problems and the $\\infty$-Polylaplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis (Reading, Tristan Pryer (Reading, UK)","submitted_at":"2016-05-25T13:47:47Z","abstract_excerpt":"In this paper we initiate the study of $2$nd order variational problems in $L^\\infty$, seeking to minimise the $L^\\infty$ norm of a function of the hessian. We also derive and study the respective PDE arising as the analogue of the Euler-Lagrange equation. Given $\\mathrm{H}\\in C^1(\\mathbb{R}^{n\\times n}_s)$, for the functional \\[ \\label{1} \\mathrm{E}_\\infty(u,\\mathcal{O})\\, =\\, \\big\\| \\mathrm{H}\\big(\\mathrm{D}^2 u\\big) \\big\\|_{L^\\infty(\\mathcal{O})}, \\ \\ \\ u\\in W^{2,\\infty}(\\Omega),\\ \\mathcal{O}\\subseteq \\Omega, \\tag{1} \\] the associated equation is the fully nonlinear 3rd order PDE \\[ \\label{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07880","kind":"arxiv","version":5},"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"}