{"paper":{"title":"Higher regularity of solutions to the singular p-Laplacean parabolic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Crispo, Paolo Maremonti","submitted_at":"2012-09-05T16:51:15Z","abstract_excerpt":"We study existence and regularity properties of solutions to the singular $p$-Laplacean parabolic system in a bounded domain $\\Omega$. The main purpose is to prove global $L^r(\\varepsilon,T;L^q(\\Omega))$, $\\varepsilon\\geq0$, integrability properties of the second spatial derivatives and of the time derivative of the solutions. Hence, for suitable $p$ and exponents $r,\\,q$, by Sobolev embedding theorems, we deduce global regularity of $u$ and $\\nabla u$ in H\\\"older spaces. Finally we prove a global pointwise bound for the solution under the assumption $p>\\frac{2n}{n+2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1038","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"}