{"paper":{"title":"Partial regularity for doubly nonlinear parabolic systems of the first type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ryan Hynd","submitted_at":"2017-02-02T04:27:04Z","abstract_excerpt":"We study solutions ${\\bf v}$ of the parabolic system of PDE $$ \\partial_t\\left(D\\psi({\\bf v})\\right)=\\text{div}DF(D{\\bf v}). $$ Here $\\psi$ and $F$ are convex functions, and this is a model equation for more general doubly nonlinear evolutions that arise in the study of phase transitions in materials. We show that if ${\\bf v}$ is a weak solution, then $D{\\bf v}$ is locally H\\\"older continuous except for possibly on a lower dimensional subset of the domain of ${\\bf v}$. Our proof is based on compactness properties of solutions, two integral identities and a fractional time derivative estimate f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00537","kind":"arxiv","version":4},"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"}