{"paper":{"title":"Generalized $\\mathbf{W^{1,1}}$-Young measures and relaxation of problems with linear growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Margarida Baia, Martin Kru\\v{z}\\'ik, Stefan Kr\\\"omer","submitted_at":"2016-11-13T17:31:03Z","abstract_excerpt":"We completely characterize generalized Young measures generated by sequences of gradients of maps from $W^{1,1}(\\Omega;\\R^M)$ where $\\Omega\\subset\\R^N$. This extends and completes previous analysis by Kristensen and Rindler where concentrations of the sequence of gradients at the boundary of $\\Omega$ were excluded. We apply our results to relaxation of non-quasiconvex variational problems with linear growth at infinity. We also link our characterization to Sou\\v{c}ek spaces \\cite{soucek}, an extension of $W^{1,1}(\\Omega;\\R^M)$ where gradients are considered as measures on $\\bar\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04160","kind":"arxiv","version":1},"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"}