{"paper":{"title":"Limiting Sobolev inequalities for vector fields and canceling linear differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen","submitted_at":"2011-04-01T15:06:48Z","abstract_excerpt":"The estimate [\\lVert D^{k-1}u\\rVert_{L^{n/(n-1)}} \\le \\lVert A(D)u \\rVert_{L^1} ] is shown to hold if and only if (A(D)) is elliptic and canceling. Here (A(D)) is a homogeneous linear differential operator (A(D)) of order (k) on (\\mathbb{R}^n) from a vector space (V) to a vector space (E). The operator (A(D)) is defined to be canceling if [\\bigcap_{\\xi \\in \\mathbb{R}^n \\setminus {0}} A(\\xi)[V]={0}.] This result implies in particular the classical Gagliardo-Nirenberg-Sobolev inequality, the Korn-Sobolev inequality and Hodge-Sobolev estimates for differential forms due to J. Bourgain and H. Brez"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0192","kind":"arxiv","version":2},"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"}