{"paper":{"title":"Schauder estimates for parabolic $p$-Laplace systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Scheven, Frank Duzaar, Naian Liao, Ugo Gianazza, Verena B\\\"ogelein","submitted_at":"2025-07-21T15:32:16Z","abstract_excerpt":"We establish the local H\\\"older regularity of the spatial gradient of bounded weak solutions $u\\colon E_T\\to\\R^k$ to the non-linear system of parabolic type \\begin{equation*}\n  \\partial_tu-\\Div\\Big( a(x,t)\\big(\\mu^2+|Du|^2\\big)^\\frac{p-2}2Du\\Big)=0\n  \\qquad\\mbox{in $E_T$}, \\end{equation*} where $p>1$, $\\mu\\in[0,1]$, and the coefficient $a\\in L^\\infty(E_T)$ is bounded below by a positive constant and is H\\\"older continuous in the space variable $x$. As an application, we prove H\\\"older estimates for the gradient of weak solutions to a doubly non-linear parabolic equation in the super-critical f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15722","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/2507.15722/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"}