Many imbeddings of functional spaces lack compactness because of the presence of a noncompact invariance, such as translation or scale invariance. Loss of compactness for bounded sequences can be effectively described with the help of this group: any bounded sequence has a subsequence consisting of a sum of decoupled "bubbles" (by group action) and a convergent remainder. This representation, called profile decomposition, exists on the functionalanalytic level, and the hard analysis is involved only in the question what is the best norm for which an absence of bubbles guarantees convergence. Successor of the classical concentration compactness, theory of profile decompositions in its present state has been applied to concentration analysis in dispersive equations (Terence Tao), yields a necessary and sufficient condition for a symmetry on a manifold to define a compact Sobolev imbedding, and shows that MoserTrudinger functional is weakly continuous on a unit ball $B$ in the Sobolev norm with an exception only for some sequences on a single threedimensional surface contained in the boundary of the unit ball.
You are here
Cocompact imbeddings and profile decompositions: functionalanalytic theory of concentration compactness.
Research Group:
Speaker:
Cyril Tintarev
Institution:
Uppsala University
Schedule:
Friday, April 19, 2013  11:00 to 12:00
Location:
A133
Abstract:
Openings
 Call of interest for positions in mathematics at SISSA
 Public Calls for Professors
 Temporary Professors/Researchers/Visiting Professors
 SISSA Mathematical Fellowships
 PostLauream Fellowships
 Research Training Fellowships
 Marie SklodowskaCurie Grants
 Open positions in MathLab
 Post Doctoral Fellowships
 PhD Scolarships
 SIS Fellowships
 Undergraduate Fellowships
 Postgraduate Fellowships
 MSc in Mathematics
 MSc in Data Science and Scientific Computing (DSSC)
 Professional Master Courses
 SISSA Mathematics Medals
Upcoming events

Pablo Alexei Gazca Orozco
Numerical computations and thermodynamically complete models for inelastic behaviour in solids
Monday, December 4, 2023  15:00

Paolo Piersanti
Variational Inequalities and their applications in elasticity and glaciology
Wednesday, December 6, 2023  16:00

Daniele Semola
Ricci Curvature, Fundamental Groups, and the Milnor Conjecture
Thursday, December 7, 2023  14:00 to 15:30

Jonathan Husson
TBA
Monday, December 11, 2023  16:00 to 17:00
Today's Lectures

09:00 to 11:00

09:00 to 11:00

09:00 to 11:00

11:00 to 13:00

11:00 to 13:00

14:00 to 18:00

14:00 to 16:00

16:00 to 18:00

16:00 to 18:00

16:15 to 18:00
Recent publications

G.P. Leonardi; G. Saracco,Rigidity and trace properties...

M. Ferrari; L. Sillari,On the Minimal Number of Solut...

M. Berti; A. Maspero; P. Ventura,Stokes waves at the critical d...

T. Beretti,On the distribution of the van...