{"paper":{"title":"Harnack estimates for degenerate parabolic equations modeled on the subelliptic p-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.AP","authors_text":"Benny Avelin, Giovanna Citti, Kaj Nystrom, Luca Capogna","submitted_at":"2013-06-24T15:11:03Z","abstract_excerpt":"We establish a Harnack inequality for a class of quasi-linear PDE modeled on the prototype {equation*}\n  \\partial_tu= -\\sum_{i=1}^{m}X_i^\\ast (|\\X u|^{p-2} X_i u){equation*} where $p\\ge 2$, $ \\ \\X = (X_1,..., X_m)$ is a system of Lipschitz vector fields defined on a smooth manifold $\\M$ endowed with a Borel measure $\\mu$, and $X_i^*$ denotes the adjoint of $X_i$ with respect to $\\mu$. Our estimates are derived assuming that (i) the control distance $d$ generated by $\\X$ induces the same topology on $\\M$; (ii) a doubling condition for the $\\mu$-measure of $d-$metric balls and (iii) the validity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5650","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"}