{"paper":{"title":"On the Numerical Approximation of $\\infty$-Harmonic Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis, Tristan Pryer (Reading, UK)","submitted_at":"2015-11-04T12:42:23Z","abstract_excerpt":"Given a map $u : \\Omega \\subseteq \\mathbb{R}^n \\longrightarrow \\mathbb{R}^N$, the $\\infty$-Laplacian is the system \\[ \\label{1} \\Delta_\\infty u \\, :=\\, \\Big(\\text{D}u \\otimes \\text{D}u + |\\text{D}u|^2 [\\text{D}u]^\\bot \\! \\otimes I \\Big) : \\text{D}^2 u\\, = \\, 0. \\tag{1} \\] \\eqref{1} is the model system of vectorial Calculus of Variations in $L^\\infty$ and arises as the \"Euler-Lagrange\" equation in relation to the supremal functional \\[ \\label{2} E_\\infty(u,\\Omega)\\, :=\\, \\| \\text{D}u \\|_{L^\\infty(\\Omega)}. \\tag{2} \\] The scalar case of \\eqref{1} has been introduced by Aronsson in the 1960s and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01308","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":""},"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"}