题目: Maximizers for fractional Caffarelli-Kohn-Nirenberg and Moser-Trudinger inequalities on the whole space.

　　时间：2018年7月30日，晚上7：00-9：00

　　地点：理学院206

　　报告人：陈露博士（北京理工大学）

　　Abstract:  

　　In this report, we first employ a new fractional Sobolev compact imbedding to establish fractional Caffarelli-Kohn-Nirenberg inequalities and existence of their extremals in subcritical case sp < n. As an application, we also proved extremals of this inequalities are ground-state solutions of some fraction p-Laplacian equation. Secondly, we use the method combining the level-sets and new compactness arguments to establish existence of extremals for fractional Moser-Trudinger inequalities with Dirichlet norm. Thirdly,we use Brezis-Lieb theorem to establish Lions concentration-compactness principle for fractional Moser-Trudinger inequalities. Finally, we establish the relationship between the best constants of the fractional Moser-Trudinger inequalities and fractional Caffarelli-Kohn-Nirenberg inequalities in the asymptotic sense.

　　报告人简介：

　　2013年起跟从北师大陆国震教授攻读硕士, 博士学位， 目前在北京理工大学任教。研究方向为多参数调和分析, 分数次方程和几何不等式. 现在主要致力于研究Moser-Trudinger 不等式和高阶CKN不等式的极值函数及其在偏微分方程中的应用。目前已经在《Transaction of the AMS》, 《Nonlinear Analysis. Theory, Methods & Applications》,  《Advanced Nonlinear Studies》,  《Communications on Pure and Applied Analysis 》 SCI杂志上以第一作者身份接收并发表了10篇文章.