Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bi-Lipschitz characteristic of quasiconformal self-mappings of the unit
  disk satisfying bi-harmonic equation   Suppose that $f$ is a $K$-quasiconformal self-mapping of the unit disk
$\mathbb{D}$, which satisfies the following: $(1)$ the biharmonic equation
$\Delta(\Delta f)=g$ $(g\in \mathcal{C}(\overline{\mathbb{D}}))$, (2) the
boundary condition $\Delta f=\varphi$ ($\varphi\in\mathcal{C}(\mathbb{T})$ and
$\mathbb{T}$ denotes the unit circle), and $(3)$ $f(0)=0$. The purpose of this
paper is to prove that $f$ is Lipschitz continuos, and, further, it is
bi-Lipschitz continuous when $\|g\|_{\infty}$ and $\|\varphi\|_{\infty}$ are
small enough. Moreover, the estimates are asymptotically sharp as $K\to 1$,
$\|g\|_{\infty}\to 0$ and $\|\varphi\|_{\infty}\to 0$, and thus, such a mapping
$f$ behaves almost like a rotation for sufficiently small $K$, $\|g\|_{\infty}$
and $\|\varphi\|_{\infty}$.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn