{"paper":{"title":"Global gradient bounds for the parabolic p-Laplacian system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Verena B\\\"ogelein","submitted_at":"2013-09-27T09:11:40Z","abstract_excerpt":"A by now classical result due to DiBenedetto states that the spatial gradient of solutions to the parabolic $p$-Laplacian system is locally H\\\"older continuous in the interior. However, the boundary regularity is not yet well understood. In this paper we prove a boundary $L^\\infty$-estimate for the spatial gradient $Du$ of solutions to the parabolic $p$-Laplacian system \\begin{equation*} \\partial_t u - \\Div \\big(|Du|^{p-2}Du\\big) = 0 \\quad\\mbox{in $\\Omega\\times(0,T)$} \\end{equation*} for $p\\ge 2$, together with a quantitative estimate. In particular, this implies the global Lipschitz regularit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7165","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"}