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SUMMARY:Non-compactness of initial data sets in high dimensions. - Bruno P
 remoselli (Université Libre de Bruxelles)
DTSTART:20160627T133000Z
DTEND:20160627T143000Z
UID:TALK66596@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>We will discuss instability and non-compactness results 
 for the conformal constraint equations in dimensions larger than six. Thes
 e equations are obtained from the classical constraint equations of the ev
 olution problem in General Relativity after a conformal change of variable
 s. The system obtained in this way is a nonlinear critical system of ellip
 tic PDEs.<br>We will show that in high dimensions blowing-up solutions of 
 this system of equations naturally appear. The method is constructive\, an
 d the construction involves topological and blow-up techniques and relies 
 on the&nbsp\;</span>a priori analysis of defects of compactness for critic
 al elliptic PDEs. A reformulation in terms of the initial-value problem wi
 ll be given.<br><br>
LOCATION:Seminar Room 1\, Newton Institute
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