{"paper":{"title":"Regularity and relaxed problems of minimizing biharmonic maps into spheres","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changyou Wang, Min-Chun Hong","submitted_at":"2004-05-04T16:33:07Z","abstract_excerpt":"For $n\\ge 5$ and $k\\ge 4$, we show that any minimizing biharmonic map from $\\Omega\\subset R^n$ to $S^k$ is smooth off a closed set whose Hausdorff dimension is at most $n-5$. When $n=5$ and $k=4$, for a parameter $\\lambda\\in [0,1]$ we introduce a $\\lambda$-relaxed energy $\\H_\\lambda$ for the Hessian energy for maps in $W^{2,2}(\\Omega,S^4)$ so that each minimizer $u_\\lambda$ of $\\H_\\lambda$ is also a biharmonic map. We also estabilish the existence and partial regularity of a minimizer of $\\H_\\lambda$ for $\\lambda\\in [0,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405059","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"}