Schwarz's Lemmas for mappings satisfying Poisson's equation

2017/08/02 by Shaolin Chen, Chen, Shaolin, Saminathan Ponnusamy +1
Mathematics · #31A05 #31B05 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1708.00715

openalex publication_date 2017/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For n≥3, m≥1 and a given continuous function g:~Ω→ℝ^m, we establish some Schwarz type lemmas for mappings f of Ω into ℝ^m satisfying the PDE: Δf=g, where Ω is a subset of ℝⁿ. Then we apply these results to obtain a Landau type theorem.

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