# [CvGmt News] seminario Tintarev 9/4

Daniele Castorina castorin at mat.uniroma2.it
Thu Apr 4 11:42:44 CEST 2013

Cari amici,

vi segnalo il prossimo seminario di ED a Tor Vergata:

Martedi' 9 Aprile 2013, h 15:15, Aula Dal Passo

Cyril Tintarev - University of Uppsala

Cocompact imbeddings and profile decompositions: functional-analytic
theory of concentration compactness.

Many imbeddings of functional spaces lack compactness because of the
presence of a non-compact 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
functional-analytic 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 Moser-Trudinger functional is weakly continuous on a unit
ball $B$ in the Sobolev norm with an exception only for some
sequences on a single three-dimensional surface contained in
$\partial B$.

--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: castorin at mat.uniroma2.it
tel: +390672594653

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