{"paper":{"title":"Blow-up analysis and boundary regularity for variationally biharmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Scheven, Serdar Altuntas","submitted_at":"2019-07-03T12:55:21Z","abstract_excerpt":"We consider critical points $u:\\Omega\\to N$ of the bi-energy\n  \\[\n  \\int_\\Omega |\\Delta u|^2\\,d x,\n  \\]\n  where $\\Omega\\subset\\mathbb{R}^m$ is a bounded smooth domain of dimension $m\\ge 5$ and $N\\subset\\mathbb{R}^L$ a compact submanifold without boundary. More precisely, we consider variationally biharmonic maps $u\\in W^{2,2}(\\Omega,N)$, which are defined as critical points of the bi-energy that satisfy a certain stationarity condition up to the boundary. For weakly convergent sequences of variationally biharmonic maps, we demonstrate that the only obstruction that can prevent the strong compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01908","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"}