主讲人 ：Chen Wenxiong (美国Yeshiva University教授)
题目：Introduction to the Method of Moving Planes
Dr Chen Wenxiong got Ph.D at Institute of Math, Academia Sinica in 1986, and pursuited postdoc study at University of Pennsylvania. Now a tennue professor at Yeshiva University in U.S. His research areas are nonlinear elliptic equations, nonlinear functional analysis and geometric analysis. He have received research grant awards from the US National Science Foundations for 17 years. Published 50 papers, many are in world prestigious journals, for eample in the Annales of Mathematics( the best math journal in the world), Math Annalen, Duke Math J, Comm Pure Appl Math, J of Diff Geom, Advances in Math, J Differential Equations, Comm Partial Differential Equs, J Geom Analysis et al. He is also a leading expert in the method of moving planes. Together with professor Congming Li, he have solved serveral open problems, includingone posed by Kazdan and one by Lieb. The citation of one of their paper is ranked top 5 among all published math papers in the year 1991, according to AMS.
In this talk, He will introduce the method of moving planes and explain how to apply it to prove symmetry of solutions of certain partial differential equations and integral equations.
The method of the moving planes was invented by the Soviet mathematician Alexanderoff in the early 1950's. Decades later, it was further developed by Serrin, Gidas, Ni, L.Nirenberg, Caffarelli, and many other leading mathematicians. It has become a powerful tool in establishing symmetry and monotonicity of solutions for partial differential equations. It can also be used to establish a priori estimates and inequalities, and prove non-existence of solutions.
Recently, he introduced the integral form of the method of moving planes and applied it to establish symmetry for solutions of integral equations and systems as well as PDEs due to the equivalences between the two. This method is quite different from the ones for PDEs. Instead of using maximum principles, some global norms are estimated.
He will try to deliver the talk in an elementary way, with the help of pictures when needed, so that even students with no previous knowledge in this area can follow.