{"paper":{"title":"A Subelliptic Analogue of Aronson-Serrin's Harnack Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Garrett Rea, Giovanna Citti, Luca Capogna","submitted_at":"2011-09-21T17:38:27Z","abstract_excerpt":"We show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE $$\\p_t u=-X_i^* A_i(x,t,u,Xu)+ B(x,t,u,Xu),$$ associated to a system of Lipschitz continuous vector fields $X=(X_1,...,X_m)$ in in $\\Om\\times (0,T)$ with $\\Om \\subset M$ an open subset of a manifold $M$ with control metric $d$ corresponding to $X$ and a measure $d\\sigma$ follows from the basic hypothesis of doubling condition and a weak Poincar\\'e inequality. We also show that such hypothesis hold for a class of Riemannian metrics $g_\\e$ collapsing to a sub-Riemannian metric $\\lim_{\\e\\to 0} g_\\e=g_0$ unifor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4596","kind":"arxiv","version":2},"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"}