Schwarz type lemma, Landau type theorem and Lipschitz type space of solutions to biharmonic equations (1801.04507v2)

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.