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arXiv · 1708.00715

Schwarz's Lemmas for mappings satisfying Poisson's equation

Shaolin Chen·Saminathan Ponnusamy
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Abstract

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.

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Shaolin Chen, Saminathan Ponnusamy. 2017-08-02. Schwarz's Lemmas for mappings satisfying Poisson's equation. https://arxiv.org/abs/1708.00715

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