{"paper":{"title":"Interpenetration of matter in plate theories obtained as Gamma-limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eris Runa, Heiner Olbermann","submitted_at":"2013-10-10T16:01:27Z","abstract_excerpt":"We consider a potential pathology in the derivation of plate theories as Gamma-limits of 3-dimensional nonlinear elasticity by Friesecke James and Muller (Comm. Pure Appl. Math., 55:1461-1506 and Arch. Ration. Mech. Anal., 180:183-236), which consists in recovery sequences of invertible maps that converge to a non-invertible limit. These pathologies have been noted by Muller and Spector (Arch. Ration. Mech. Anal. 131:1-66) in a different context. Using a combination of degree theory, the approximation of Sobolev functions by Lipschitz functions and geometric rigidity we show that the potential"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2865","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"}