报告题目：Nonlinear Equations Involving the Fractional Laplacians
主 讲 人：陈 文 雄
In this talk, we will consider nonlinear nonlocal equations, in particular, the ones involving the fractional Laplacian. This is a typical nonlocal operator which is quite different from the local operators, such as the regular Laplacian. Hence many traditional methods on elliptic equations no longer work here. We will start from the definition of the fractional Laplacian, use simple examples to illustrate its nonlocal-ness and how we approach it differently. Then we will gradually introduce the new ideas and results in this area including our current results on asymptotic radial symmetry and monotonicity of positive solutions for nonlinear parabolic fractional equations.
陈文雄，博士生导师，美国Yeshiva大学数学系终身教授，Communications on Pure and Applied Analysis，Nonlinear Analysis TMA编委，是非线性偏微分方程、非线性泛函分析、几何分析等领域著名华人学者。在数学顶级期刊Annals of Math, J. of Diff. Geom, Comm. Pure and Appl. Math, Duke Math. J, Advances in Math, Arch. Rat. Mech. Anal, J. Diff. Equa, Trans. AMS等发表论文50余篇。其中与Congming Li教授合作发表在Duke Math. J.上的文章已被引用500余次。