{"paper":{"title":"A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Flaviana Iurlano, Matteo Focardi, Sergio Conti","submitted_at":"2018-04-26T08:57:24Z","abstract_excerpt":"We prove partial regularity for minimizers to elasticity type energies in the nonlinear framework {with $p$-growth, $p>1$,} in dimension $n\\geq 3$. It is an open problem in such a setting either to establish full regularity or to provide counterexamples. In particular, we give an estimate on the Hausdorff dimension of the potential singular set by proving that is strictly less than {$n-(p^*\\wedge 2)$, and actually $n-2$ in the autonomous case} (full regularity is well-known in dimension $2$).\n  The latter result is instrumental to establish existence for the strong formulation of Griffith type"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09945","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"}