{"paper":{"title":"A geometric tangential approach to sharp regularity for degenerate evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eduardo V. Teixeira, Jos\\'e Miguel Urbano","submitted_at":"2013-07-03T16:02:19Z","abstract_excerpt":"That the weak solutions of degenerate parabolic pdes modelled on the inhomogeneous $p-$Laplace equation $$ u_t - \\mathrm{div} \\left(|\\nabla u|^{p-2} \\nabla u \\right) = f \\in L^{q,r}, \\quad p>2 $$ are $C^{0,\\alpha}$, for some $\\alpha \\in (0,1)$, is known for almost 30 years. What was hitherto missing from the literature was a precise and sharp knowledge of the H\\\"older exponent $\\alpha$ in terms of $p, q, r$ and the space dimension $n$. We show in this paper that $$ \\alpha = \\frac{(pq-n)r-pq}{q[(p-1)r-(p-2)]}, $$ using a method based on the notion of geometric tangential equations and the intri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1057","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"}