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数学学科现代分析及其应用研究所学术报告(陈文雄 美国Yeshiva大学)

发布者:戴 情   发布时间:2021-11-15  浏览次数:137

非线性分析与偏微分方程著名学者报告

报告题目Liouville Theorems for Fractional Parabolic Equations 

报告人陈文雄美国Yeshiva大学

会议时间:1118日(周),9:30-10:30

腾讯会议ID:  245 333 121

https://meeting.tencent.com/dm/8TDPVGxvASJl

 

摘要We establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum principles for antisymmetric functions in unbounded domains, in which we remarkably weaken the usual decay condition u → 0 at infinity to a polynomial growth on u by constructing proper auxiliary functions. Then we derive monotonicity for the solutions in a half space ℝn+× ℝ and obtain some new connections between the nonexistence of solutions in a half space ℝn+× ℝ and in the whole space ℝn−1 × ℝ and therefore prove the corresponding Liouville type theorems. To overcome the difficulty caused by the nonlocality of the fractional Laplacian, we introduce several new ideas which will become useful tools in investigating qualitative properties of solutions for a variety of nonlocal parabolic problems.

 

报告人简介陈文雄,教授,博士生导师。美国纽约Yeshiva大学终身教授,数学系主任,南开大学特聘讲座教授(天津市千人),国际知名的数学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。 曾多次获得美国国家科学基金奖。担任Nonlinear Analysis: Theory, Methods & Applications “Communication on Pure and Applied Analysis”的编委数学顶级期刊Annals of Math, J. Diff. Geom,  Comm. Pure and Appl. Math,  Duke Math.  J, Adv. Math,  Arch. Rat. Mech.Anal,  J. Diff. Equ, 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”引用高达750以上。出版学术专著《Methods on Nonlinear Elliptic EquationsThe Fractional Laplacian》。

 

邀请人:非线性分析与PDE团队