{"paper":{"title":"A New Extension of Serrin's Lower Semicontinuity Theorem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hu Xiaohong, Zhang Shiqing","submitted_at":"2012-05-13T03:50:18Z","abstract_excerpt":"In this paper, we present a new extension of the famous Serrin's lower semicontinuity theorem for the variational functional $\\int_{\\Omega}f(x,u,u')dx$,we prove its lower semicontinuity in $W_{loc}^{1,1}(\\Omega)$ with respect to the strong $L_{loc}^{1}$ topology assuming that the integrand $f(x,s,\\xi)$ has the usual continuity on all the three variables and the convexity property on the variable $\\xi$ and the local absolute continuity on the variable $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2826","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"}