{"paper":{"title":"The div-curl lemma for sequences whose divergence and curl are compact in W^{-1,1}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georg Dolzmann, Sergio Conti, Stefan M\\\"uller","submitted_at":"2009-07-02T14:55:38Z","abstract_excerpt":"It is shown that $u_k \\cdot v_k$ converges weakly to $u\\cdot v$ if $u_k\\weakto u$ weakly in $L^p$ and $v_k\\weakly v$ weakly in $L^q$ with $p, q\\in (1,\\infty)$, $1/p+1/q=1$, under the additional assumptions that the sequences $\\Div u_k$ and $\\curl v_k$ are compact in the dual space of $W^{1,\\infty}_0$ and that $u_k\\cdot v_k$ is equi-integrable. The main point is that we only require equi-integrability of the scalar product $u_k\\cdot v_k$ and not of the individual sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0397","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"}