{"paper":{"title":"A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in $W^{1,n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gianluca Orlando, Vito Crismale","submitted_at":"2017-07-12T17:10:09Z","abstract_excerpt":"In this paper we prove a lower semicontinuity result of Reshetnyak type for a class of functionals which appear in models for small-strain elasto-plasticity coupled with damage. To do so we characterise the limit of measures $\\alpha_k\\,\\mathrm{E}u_k$ with respect to the weak convergence $\\alpha_k\\rightharpoonup \\alpha$ in $W^{1,n}(\\Omega)$ and the weak$^*$ convergence $u_k\\stackrel{*}\\rightharpoonup u$ in $BD(\\Omega)$, $\\mathrm{E}$ denoting the symmetrised gradient. A concentration compactness argument shows that the limit has the form $\\alpha\\,\\mathrm{E}u+\\eta$, with $\\eta$ supported on an at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03801","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"}