{"paper":{"title":"Harnack inequality for hypoelliptic second order partial differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessia E. Kogoj, Sergio Polidoro","submitted_at":"2015-09-17T13:18:08Z","abstract_excerpt":"We consider nonnegative solutions $u:\\Omega\\longrightarrow \\mathbb{R}$ of second order hypoelliptic equations \\begin{equation*} \\mathscr{L} u(x) =\\sum_{i,j=1}^n \\partial_{x_i} \\left(a_{ij}(x)\\partial_{x_j} u(x) \\right) + \\sum_{i=1}^n b_i(x) \\partial_{x_i} u(x) =0, \\end{equation*} where $\\Omega$ is a bounded open subset of $\\mathbb{R}^{n}$ and $x$ denotes the point of $\\Omega$. For any fixed $x_0 \\in \\Omega$, we prove a Harnack inequality of this type $$\\sup_K u \\le C_K u(x_0)\\qquad \\forall \\ u \\ \\mbox{ s.t. } \\ \\mathscr{L} u=0, u\\geq 0,$$ where $K$ is any compact subset of the interior of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05245","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"}