报告题目：0n asymptotically sharp bi-Lipschitz inequalities of quasiconformal mappings satisfying inhomogeneous polyharmonic equations

报 告 人：陈少林教授（衡阳师范学院）

报告时间：2021年5月21日  15:00-16:00

报告地点：数统院5楼数学研究中心智慧教室

报告摘要：

For two constants K≥1 and K0≥0, suppose that f is a (K, K0)-quasiconformal self-mapping of the unit disk D, which satifies the fllowing: (1) the inhomogencous polyharmonice equation Δnf=Δ(Δn-1f)=φn in D(φn∈C(D)), (2) the boundary conditions Δn-1f=φn-1,...Δlf=φ1 on T(φj∈C(T)for j∈{1,...,n- 1} and T denotes the unit cirele), 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 small enough for j∈{1,...,n}. Morcover, the estimates are asymtically shamp asK→1+, K0→0+ and ||φj||∞→0+ forj∈{1,...,n}.

报告人简介：

陈少林，衡阳师范学院教授，湖南省青年骨干教师。曾在芬兰阿尔托大学、芬兰赫尔辛基大学、芬兰图尔库大学、印度马德拉斯理工学院和印度拉马努金（Ramanu jan）数学研究所做访问学者。