{"paper":{"title":"Thin-film limits of functionals on A-free vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carolin Kreisbeck, Filip Rindler","submitted_at":"2011-05-19T12:05:20Z","abstract_excerpt":"This paper deals with variational principles on thin films subject to linear PDE constraints represented by a constant-rank operator $\\mathcal{A}$. We study the effective behavior of integral functionals as the thickness of the domain tends to zero, investigating both upper and lower bounds for the $\\Gamma$-limit. Under certain conditions we show that the limit is an integral functional and give an explicit formula. The limit functional turns out to be constrained to $\\mathcal{A}_0$-free vector fields, where the limit operator $\\mathcal{A}_0$ is in general not of constant rank. This result ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3848","kind":"arxiv","version":3},"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"}