Schwarz type lemma, Landau type theorem and Lipschitz type space of solutions to biharmonic equations

Shaolin Chen; Peijin Li; Xiantao Wang

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arXiv · 1801.04507

Schwarz type lemma, Landau type theorem and Lipschitz type space of solutions to biharmonic equations

Shaolin Chen·Peijin Li·Xiantao Wang

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Abstract

The purpose of this paper is to study the properties of the solutions to the biharmonic equations: $\Delta(\Delta f)=g$, where $g:$ $\overline{\mathbb{D}}\rightarrow\mathbb{C}$ is a continuous function and $\overline{\mathbb{D}}$ denotes the closure of the unit disk $\mathbb{D}$ in the complex plane $\mathbb{C}$. In fact, we establish the following properties for those solutions: Firstly, we establish the Schwarz type lemma. Secondly, by using the obtained results, we get a Landau type theorem. Thirdly, we discuss their Lipschitz type property.

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BibTeX RIS

Shaolin Chen, Peijin Li, Xiantao Wang. 2018-01-14. Schwarz type lemma, Landau type theorem and Lipschitz type space of solutions to biharmonic equations. https://arxiv.org/abs/1801.04507

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