报告题目：An introduction to the fractional Laplacian and qualitative properties of solutions
时 间：2023年3月16日（星期四）上午8:00
地 点：腾讯会议 ID：879 258 806
主 办：数学与统计学院、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、福建师范大学数学研究中心
参加对象：感兴趣的老师和研究生
报告摘要：In this talk, we will first introduce the fractional Laplacian,discuss its fundamental properties, and elaborate its major differences from the classical Laplacian operator. Then we will list some recent developments in the study of qualitative properties including symmetry,asymptotic symmetry, and monotonicity of solutions for nonlinear fractional elliptic and parabolic equations such as 
and
There have been a series of results in literature if the fractional Laplacian is replaced by the classical Laplacian in the above problems.However, due to its non-locality, many traditional approaches no longer work here. We will use simple examples to illustrate how to overcome such a difficulty. We will try to make this talk as elementary as possible so that even the beginners in this field can follow.
报告人简介：陈文雄，叶史瓦大学终身教授，数学系主任，博士生导师，南开大学特聘讲座教授。多次获得美国国家科学基金奖。陈文雄教授是偏微分方程和几何分析的杰出专家，研究领域包括非线性偏微分方程、几何分析、非线性泛函分析等。陈教授担任《Communications on Pure and Applied Analysis》杂志的编委，被多个 SCI 期刊评为优秀审稿人，研究方向为非线性偏微分方程，目前以分数阶 Laplace 方程为主。他曾先后在在数学顶级期刊 Annals of Math, of Diff. Geom., Comm. Pure and Appl. Math, Duke Math. J, Advance in Math, Arch. Rat. Mech. Anal.等发表论文 80 余篇，并出版了三本专著，他引已达五千余次，其中在 Duke Math. J.上发表的名为《Classification of solutions of some nonlinear elliptic equations》的论文被引高达 1000 余次。在 CPAM 上发表的名为《Classificationfor the solutions of integral equations一篇被引高达 400次以上。近年来，他在《Advancesin Mathematics》发表的文章中有三篇被列为高被引（HighlyCited)。出版学术专著《Methods on Nonlinear Elliptic Equations》与《The Fractional Laplacian》。