{"paper":{"title":"Lipschitz continuity of solutions of Poisson equations in metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Renjin Jiang","submitted_at":"2010-04-07T14:41:41Z","abstract_excerpt":"Let $(X,d)$ be a pathwise connected metric space equipped with an Ahlfors $Q$-regular measure $\\mu$, $Q\\in[1,\\infty)$. Suppose that $(X,d,\\mu)$ supports a 2-Poincar\\'e inequality and a Sobolev-Poincar\\'e type inequality for the corresponding \"Gaussian measure\". The author uses the heat equation to study the Lipschitz regularity of solutions of the Poisson equation $\\Delta u=f$, where $f\\in L^p_\\loc$. When $p>Q$, the local Lipschitz continuity of $u$ is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1101","kind":"arxiv","version":3},"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"}