{"paper":{"title":"On regularity theory for n/p-harmonic maps into manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Armin Schikorra, Francesca Da Lio","submitted_at":"2017-09-07T16:10:31Z","abstract_excerpt":"In this paper we continue the investigation of the regularity of the so-called weak $\\frac{n}{p}$-harmonic maps in the critical case. These are critical points of the following nonlocal energy \\[ {\\mathcal{L}}_s(u)=\\int_{\\mathbb{R}^n}| ( {-\\Delta})^{\\frac{s}{2}} u(x)|^p dx\\,, \\] where $u\\in \\dot{H}^{s,p}(\\mathbb{R}^n,\\mathcal{N})$ and ${\\mathcal{N}}\\subset\\mathbb{R}^N$ is a closed $k$ dimensional smooth manifold and $s=\\frac{n}{p}$. We prove H\\\"older continuity for such critical points for $p \\leq 2$. For $p > 2$ we obtain the same under an additional Lorentz-space assumption. The regularity t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02329","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"}