{"paper":{"title":"Schwarz's Lemmas for mappings satisfying Poisson's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Saminathan Ponnusamy, Shaolin Chen","submitted_at":"2017-08-02T12:07:08Z","abstract_excerpt":"For $n\\geq3$, $m\\geq1$ and a given continuous function $g:~\\Omega\\rightarrow\\mathbb{R}^{m}$, we establish some Schwarz type lemmas for mappings $f$ of $\\Omega$ into $\\mathbb{R}^{m}$ satisfying the PDE: $\\Delta f=g$, where $\\Omega$ is a subset of $\\mathbb{R}^{n}$. Then we apply these results to obtain a Landau type theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00715","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"}