腾讯会议ID：148 925 446
(一) 报告人：郑高峰 教授 华中师范大学
报告题目：The Lamm-Riviere System: L^p Regularity Theory
报告摘要：Motived by the heat flow and bubble analysis of biharmonic mappings, we study
further regularity issues of the fourth order Lamm-Rivière system
∆^2 u=∆(V ·∇u)+div(w∇u)+(∇ω+F)·∇u+f
in dimension four, with an inhomogeneous term f which belongs to some natural
function space. We obtain optimal higher order regularity and sharp Hölder continuity of weak solutions.
Among several applications, we derive weak compactness for
sequences of weak solutions with uniformly bounded energy, which generalizes the
weak convergence theory of approximate biharmonic mappings. This is a joint work with Prof. Chang-Yu Guo and Prof. Chang-Lin Xiang.
（二）报告人：熊金钢 教授 北京师范大学
报告题目：Bubbling and extinction profiles of the critical fast diffusion equation in bounded domain
报告摘要：I will report my recent joint work with T. Jin about a Sobolev critical fast diffusion equation in bounded domains with the Brezis-Nirenberg effect. We obtain extinction profiles of its positive solutions, and show that the convergence rates of the relative error in regular norms are at least polynomial. Exponential decay rates are proved for generic domains. Our proof makes use of its regularity estimates, a curvature type evolution equation, as well as blow up analysis. Results for Sobolev subcritical fast diffusion equations are also obtained.