{"paper":{"title":"H\\\"older Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Scheven, Frank Duzaar, Naian Liao, Ugo Gianazza, Verena B\\\"ogelein","submitted_at":"2023-05-15T11:11:10Z","abstract_excerpt":"This paper is devoted to studying the local behavior of non-negative weak solutions to the doubly non-linear parabolic equation \\begin{equation*}\n  \\partial_t u^q -\n  \\text{div}\\big(|D u|^{p-2}D u\\big)\n  =\n  0 \\end{equation*} in a space-time cylinder. H\\\"older estimates are established for the gradient of its weak solutions in the super-critical fast diffusion regime $0<p-1< q<\\frac{N(p-1)}{(N-p)_+}$ where $N$ is the space dimension. Moreover, decay estimates are obtained for weak solutions and their gradient in the vicinity of possible extinction time. Two main components towards these regula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08539","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.08539/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}