[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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