{"paper":{"title":"Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Filip Rindler","submitted_at":"2010-08-12T10:51:32Z","abstract_excerpt":"We establish a general weak* lower semicontinuity result in the space $\\BD(\\Omega)$ of functions of bounded deformation for functionals of the form $$\\Fcal(u) := \\int_\\Omega f \\bigl(x, \\Ecal u \\bigr) \\dd x + \\int_\\Omega f^\\infty \\Bigl(x, \\frac{\\di E^s u}{\\di \\abs{E^s u}} \\Bigr) \\dd \\abs{E^s u} + \\int_{\\partial \\Omega} f^\\infty \\bigl(x, u|_{\\partial \\Omega} \\odot n_\\Omega \\bigr) \\dd \\Hcal^{d-1}$$, $u \\in \\BD(\\Omega)$. The main novelty is that we allow for non-vanishing Cantor-parts in the symmetrized derivative $Eu$. The proof is accomplished via Jensen-type inequalities for generalized Young m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2089","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"}