{"paper":{"title":"Approximation in higher-order Sobolev spaces and Hodge systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Emmanuel Russ, Pierre Bousquet, Po-Lam Yung, Yi Wang","submitted_at":"2017-09-06T10:58:45Z","abstract_excerpt":"Let $d\\geq 2$ be an integer, $1\\leq l\\leq d-1$ and $\\varphi$ be a differential $l$-form on ${\\mathbb R}^d$ with $\\dot{W}^{1,d}$ coefficients. It was proved by Bourgain and Brezis (\\cite[Theorem 5]{MR2293957}) that there exists a differential $l$-form $\\psi$ on ${\\mathbb R}^d$ with coefficients in $L^{\\infty}\\cap \\dot{W}^{1,d}$ such that $d\\varphi=d\\psi$. Bourgain and Brezis also asked whether this result can be extended to differential forms with coefficients in the fractional Sobolev space $\\dot{W}^{s,p}$ with $sp=d$. We give a positive answer to this question, in the more general context of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01762","kind":"arxiv","version":3},"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"}