{"paper":{"title":"$\\mathcal{D}$-solutions to the system of vectorial Calculus of Variations in $L^\\infty$ via the singular value problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni Pisante, Gisella Croce, Nikos Katzourakis","submitted_at":"2016-04-15T07:37:13Z","abstract_excerpt":"For $\\mathrm{H} \\in C^2(\\mathbb{R}^{N \\times n})$ and $u : \\Omega \\subseteq \\mathbb{R}^n \\to \\mathbb{R}^N$, consider the system \\[ \\label{1}\\mathrm{A}\\_\\infty  u\\, :=\\,\\Big(\\mathrm{H}\\_P \\otimes \\mathrm{H}\\_P + \\mathrm{H}[\\mathrm{H}\\_P]^\\bot \\mathrm{H}\\_{PP}\\Big)(\\mathrm{D} u): \\mathrm{D}^2 u\\, =\\,0. \\tag{1}\\]We construct $\\mathcal{D}$-solutions to the Dirichlet problem for (1), an apt notion of generalised solutions recently proposed for fully nonlinear systems. Our $\\mathcal{D}$-solutions are $W^{1,\\infty}$-submersions and are obtained without any convexity hypotheses for $\\mathrm{H}$, throu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04385","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"}