Cocompact imbeddings and profile decompositions.

SpeakerProf. Cyril Tintarev ( Uppsala University

 

Date15:00-17:00 pm, October 30, 2014

 

PlaceConference Room 304, Department of Mathematical Sciences

 

Title 1Cocompact imbeddings and profile decompositions.

AbstractAbstract):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.

 

Title 2 Is Moser-Trudinger nonlinearity a true critical nonlinearity? 

AbstractAbstract):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.

 

ContactWenming Zou