{"paper":{"title":"Fractional Sobolev Regularity for the Brouwer Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Camillo De Lellis, Dominik Inauen","submitted_at":"2017-02-07T16:07:30Z","abstract_excerpt":"We prove that if $\\Omega\\subset \\mathbb R^n$ is a bounded open set and $n\\alpha> {\\rm dim}_b (\\partial \\Omega) = d$, then the Brouwer degree deg$(v,\\Omega,\\cdot)$ of any H\\\"older function $v\\in C^{0,\\alpha}\\left (\\Omega, \\mathbb R^{n}\\right)$ belongs to the Sobolev space $W^{\\beta, p} (\\mathbb R^n)$ for every $0\\leq \\beta < \\frac{n}{p} - \\frac{d}{\\alpha}$. This extends a summability result of Olbermann and in fact we get, as a byproduct, a more elementary proof of it. Moreover we show the optimality of the range of exponents in the following sense: for every $\\beta\\geq 0$ and $p\\geq 1$ with $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02075","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"}