数学科学系

Department of Mathematical Sciences

数学系综合学术报告 1-2

数学系综合学术报告 1-2

(非线性分析和微分方程研究团队学术报告)

 

报告人(speaker)Prof. Cyril Tintarev ( 瑞典 Uppsala University 数学系,教授)

 

时间(time)20141030日(星期四) 1500-1700pm

 

地点(Venue):理科楼数学系A304

 

报告题目1 (Title 1)Cocompact imbeddings and profile decompositions.

摘要(Abstract):we present a functional-analytic formailization of concentration compactness in Banach spaces with applications to specific functional spaces. A continuous imbedding cannot be compact if both norms are invariant with respect to the same non-compact (in strong topology) group of linear isometries. Such non-compact imbedding may be cocompact with respect to this group, which allows identify concentrations as elements of the space subjected to a non-compact sequence of group actions. Subtraction of such concentrating sequence may result in a remainder convergent in the target space. Besides the classical example of translations and dilations for spaces of Sobolev type, profile decompositions are known for other transformations in connection to Moser-Trudinger as well as Strichartz imbeddings.

 

 

报告题目2 (Title 2) Is Moser-Trudinger nonlinearity a true critical nonlinearity? 

摘要(Abstract):Unlike the Sobolev critical nonlinearity in higher dimensions, Moser-Trudinger functional is weakly continuous except on very specific concentrating sequences. This indicates that Moser-Trudinger inequality is not optimal, and indeed, it can be improved. We also discuss the scaling properties of the Moser-Trudinger nonlinearity and the analogs of Talenti solution.

 

 

报告人简介:Cyril Tintarev是瑞典Uppsala University 数学系教授,

是该国在变分与拓扑方法和PDE方面的主要专家之一。  

在集中紧性原理和非线性椭圆方程的研究方面取得重要成果。

著有专著《Concentration Compactness》(Imperial College Press2007)。

 

联系人:邹文明