Schwarz's Lemmas for mappings satisfying Poisson's equation

Abstract

For $n\ge 3$, $m\ge 1$ and a given continuous function $g:\Omega \to {\mathbb{R}}^m$, 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.

14 pages