{"paper":{"title":"A matrix differential Harnack estimate for a class of ultraparabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Hong Huang","submitted_at":"2013-06-20T10:25:13Z","abstract_excerpt":"Let $u$ be a positive solution of the ultraparabolic equation \\begin{equation*} \\partial_t u=\\sum_{i=1}^n \\partial_{x_i}^2 u+\\sum_{i=1}^k x_i\\partial_{x_{n+i}}u \\hspace{8mm} \\mbox{on} \\hspace{4mm} \\mathbb{R}^{n+k}\\times (0,T), \\end{equation*} where $1\\leq k\\leq n$ and $0<T \\leq +\\infty$. Assume that $u$ and its derivatives (w.r.t. the space variables) up to the second order are bounded on any compact subinterval of $(0,T)$. Then the difference $H(\\log u)- H(\\log f)$ of the Hessian matrices of $\\log u$ and of $\\log f$ (both w.r.t. the space variables) is non-negatively definite, where $f$ is th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4810","kind":"arxiv","version":4},"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"}