{"paper":{"title":"Sequential Weak Approximation for Maps of Finite Hessian Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Robert Hardt, Tristan Rivi\\`ere","submitted_at":"2013-05-31T07:22:53Z","abstract_excerpt":"Consider the space $W^{2,2}(\\Omega;N)$ of second order Sobolev mappings $\\ v\\ $ from a smooth domain $\\Omega\\subset\\R^m$ to a compact Riemannian manifold $N$ whose Hessian energy $\\int_\\Omega |\\nabla^2 v|^2\\, dx$ is finite. Here we are interested in relations between the topology of $N$ and the $W^{2,2}$ strong or weak approximability of a $W^{2,2}$ map by a sequence of smooth maps from $\\Omega$ to $N$. We treat in detail $W^{2,2}(\\B^5,S^3)$ where we establish the \\underline{sequential weak} $W^{2,2}$ density of $W^{2,2}(\\B^5,S^3)\\cap{\\mathcal C}^\\infty$. The strong $W^{2,2}$ approximability o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7315","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":""},"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"}