期刊论文

Chen, Shaolin

英文

JOURNAL OF GEOMETRIC ANALYSIS

1050-6926

2021

31

5

4865-4905

10.1007/s12220-020-00460-9

We are grateful to the referee for her/his comments and suggestions. This research was partly supported by the exchange project for the third regular session of the China-Montenegro Committee for Cooperation in Science and Technology (No. 3-13), the Hunan Provincial Education Department Outstanding Youth Project (No. 18B365), the Science and Technology Plan Project of Hengyang City (No. 2018KJ125), the National Natural Science Foundation of China (No. 11571216), the Science and Technology Plan Project of Hunan Province (No. 2016TP1020), the Science and Technology Plan Project of Hengyang City (No. 2017KJ183), and the Application-Oriented Characterized Disciplines, Double First-Class University Project of Hunan Province (Xiangjiaotong [2018]469).

本校为第一且通讯机构

For two constants K≥ 1 and K′≥ 0 , suppose that f is a (K, K′) -quasiconformal self-mapping of the unit disk D, which satisfies the following: (1) the inhomogeneous polyharmonic equation Δ nf= Δ (Δ n-1f) = φn in D(φn∈ C(D¯)) , (2) the boundary conditions Δn-1f=φn-1,…,Δ1f=φ1 on T (φj∈ C(T) for j∈ { 1 , … , n- 1 } and T denotes the unit circle), and (3) f(0) = 0 , where n≥ 2 is an integer. The main aim of this paper is to prove that f is Lipschitz continuous, and, further, it is bi-Lipschitz continuous when ‖ φj‖ ∞ are sm...