{"paper":{"title":"Lp-gradient harmonic maps into spheres and SO(N)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra","submitted_at":"2014-04-03T14:05:18Z","abstract_excerpt":"We consider critical points of the energy $E(v) := \\int_{\\mathbb{R}^n} |\\nabla^s v|^{\\frac{n}{s}}$, where $v$ maps locally into the sphere or $SO(N)$, and $\\nabla^s = (\\partial_1^s,\\ldots,\\partial_n^s)$ is the formal fractional gradient, i.e. $\\partial_\\alpha^s$ is a composition of the fractional laplacian with the $\\alpha$-th Riesz transform. We show that critical points of this energy are H\\\"older continuous.\n  As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of $n$-harmonic maps into the sphere, which is interesting on its own."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0913","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"}