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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.2089","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-12T10:51:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1eea139749a5302ce04678e08cae22c86d8080ea72a1d9e3c95b04b04ebc1155","abstract_canon_sha256":"a3aadf660f3498dc244b3d81de9c3d4aa87586de0b8c5f55054e23c6efd8d1d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:49.072720Z","signature_b64":"qNMqpP1ZQYPOWQox02aruNziQLWiVa+zBTtxQO252GWyHKj05aNocJ8/4X2hG1mqMIGfGBJYcHFDf4SUv903DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b517e1617e5e6f77a817cb6d1b9f6ee71b21f52234c2bbaa659a41320739067","last_reissued_at":"2026-05-18T02:05:49.072091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:49.072091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $Eu$. 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