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The fractional Laplacian and the fractional p-Laplacian

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讲座题目:The fractional Laplacian and the fractional p-Laplacian
讲座人: 陈文雄 教授
讲座时间:15:30
讲座日期:2018-6-27
地点:长安校区文津楼数学与信息科学学院学术交流厅

讲座内容简介:The fractional Laplacian is a non-local pseudo-differential operator defined by a singular integral. It is quite different from the traditional (local) differential operators.In this talk, we will use simple examples to illustrate the essential differences between the local and nonlocal operators, such as the uniqueness, maximum principles, and boundary regularities. We will show how to construct a sub-solution to prove a Hopf lemma.We will introduce the fractional p-Laplacian, the radial symmetry of solutions, the idea of direct method of moving planes on nonlinear equations involving such operators, the Hopf lemma, and the regularities.

讲座人简介:陈文雄教授现任美国叶史瓦大学数学系终身教授,叶史瓦大学数学系主任,国际数学期刊“Nonlinear Analysis, Series A, Theory and Applications ”和“Communication on Pure and Applied Analysis”的编辑。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分方程、几何分析、非线性泛函分析等,主要研究高阶椭圆方程解的对称性,不存在性及格林函数表示,非线性方程正解的分类(用移动球面或平面法),几何不等式,黎曼流形上正解的性质等。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60余篇。其中与Congming Li教授合作发表在Duke Math. J.上的文章“Classification of solutions of some nonlinear elliptic equations”已被引用达445次。发表在“Comm. Pure Appl. Math.”上的文章“Classification of solutions for an integral equation”已被引用达288次。

 

 
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