{"paper":{"title":"Young measures supported on invertible matrices","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Barbora Bene\\v{s}ov\\'a, Gabriel Path\\'o, Martin Kru\\v{z}\\'ik","submitted_at":"2011-03-15T09:00:52Z","abstract_excerpt":"Motivated by variational problems in nonlinear elasticity depending on the deformation gradient and its inverse, we completely and explicitly describe Young measures generated by matrix-valued mappings $\\{Y_k\\}_{k\\in\\N} \\subset L^p(\\O;\\R^{n\\times n})$, $\\O\\subset\\R^n$, such that $\\{Y_k^{-1}\\}_{k\\in\\N} \\subset L^p(\\O;\\R^{n\\times n})$ is bounded, too. Moreover, the constraint $\\det Y_k>0$ can be easily included and is reflected in a condition on the support of the measure. This condition typically occurs in problems of nonlinear-elasticity theory for hyperelastic materials if $Y:=\\nabla y$ for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2859","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"}