skip to content
 

Non-compactness of initial data sets in high dimensions.

Presented by: 
Bruno Premoselli Université Libre de Bruxelles
Date: 
Monday 27th June 2016 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
We will discuss instability and non-compactness results for the conformal constraint equations in dimensions larger than six. These equations are obtained from the classical constraint equations of the evolution problem in General Relativity after a conformal change of variables. The system obtained in this way is a nonlinear critical system of elliptic PDEs.
We will show that in high dimensions blowing-up solutions of this system of equations naturally appear. The method is constructive, and the construction involves topological and blow-up techniques and relies on the 
a priori analysis of defects of compactness for critical elliptic PDEs. A reformulation in terms of the initial-value problem will be given.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons