{"paper":{"title":"Partial regularity for type two doubly nonlinear parabolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ryan Hynd","submitted_at":"2017-04-19T03:43:43Z","abstract_excerpt":"We study weak solutions ${\\bf v}:U\\times (0,T)\\rightarrow \\mathbb{R}^m$ of the nonlinear parabolic system $$ D\\psi({\\bf v}_t)=\\text{div}DF(D{\\bf v}), $$ where $\\psi$ and $F$ are convex functions. This is a prototype for more general doubly nonlinear evolutions which arise in the study of structural properties of materials. Under the assumption that the second derivatives of $F$ are H\\\"older continuous, we show that $D^2{\\bf v}$ and ${\\bf v}_t$ are locally H\\\"older continuous except for possibly on a lower dimensional subset of $U\\times (0,T)$. Our approach relies on two integral identities, de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05602","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"}