{"paper":{"title":"An integrability result for $L^p$-vectorfields in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Mircea Petrache","submitted_at":"2010-07-05T13:49:38Z","abstract_excerpt":"We prove that if $p>1$ then the divergence of a $L^p$-vectorfield $V$ on a 2-dimensional domain $\\Omega$ is the boundary of an integral 1-current, if and only if $V$ can be represented as the rotated gradient $\\nabla^\\perp u$ for a $W^{1,p}$-map $u:\\Omega\\to S^1$. Such result extends to exponents $p>1$ the result on distributional Jacobians of Alberti, Baldo, Orlandi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0681","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"}