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)：2014年10月30日（星期四）15：00-17：00pm

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 Press，2007）。

联系人：邹文明