{"paper":{"title":"Lower semicontinuity via W^{1,q}-quasiconvexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Jean-Philippe Mandallena","submitted_at":"2011-06-14T21:31:03Z","abstract_excerpt":"We isolate a general condition, that we call \"localization principle\", on the integrand L:\\MM\\to[0,\\infty], assumed to be continuous, under which W^{1,q}-quasiconvexity with q\\in[1,\\infty] is a sufficient condition for I(u)=\\int_\\Omega L(\\nabla u(x))dx to be sequentially weakly lower semicontinuous on W^{1,p}(\\Omega;\\RR^m) with p\\in]1,\\infty[. Some applications are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2828","kind":"arxiv","version":7},"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"}