报告名称：Some recent progress on a fourth order elliptic systems

主办单位：英国威廉希尔体育公司

报告专家：向长林

专家所在单位：长江大学

报告时间：2020年11月6日14：30-16：30

报告地点：腾讯会议（会议ID：367 990 781）

专家简介：向长林，博士，长江大学数学与信息学院副教授。2015年9月博士毕业于芬兰于韦斯屈莱大学数学系，师从钟晓教授。2016年8月完成博士后研究。2016年9月至今任教于长江大学信息与数学学院。主要研究领域为椭圆型偏微分方程(组)和变分法,几何分析。在SCI期刊上发表过多篇文章。主持国家自然科学青年基金一项。

报告摘要：Since the seminar work on weakly harmonic mappings of Helein in 1991 around, there have been great progress in the field of conformally invariant variational problems. In particular, the 2007 work of T. Riviere established a very powerful new tool to study regularity of weak solutions to a very general second order elliptic systems. His work was soon extend by Lamm and himself in 2008 to a fourth order elliptic system which can model fourth order conformally invariant variational problems such as biharmonic mappings and related. However, in the 2008 work, they only proved continuity of the forth order system, left open whether the weak solution is H\"older continuous or not. In this talk, I will discuss some recent progress in this respect, including not only the H\"older continuity theory, but also $L^{p}$ theory of this system as well. This is a joint work with Chang-Yu Guo (Shangdong Univ.) and Gao-Feng Zheng (Central China Normal Univ.).

邀请人：毛井