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Cari amici,<br>
<br>
vi segnalo il prossimo seminario di ED a Tor Vergata:<br>
<br>
<h2>Martedi' 9 Aprile 2013, h 15:15, Aula Dal Passo
</h2>
<h2>Cyril Tintarev - University of Uppsala
</h2>
<h2>Cocompact imbeddings and profile decompositions:
functional-analytic theory of concentration compactness.<br>
<br>
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 $\partial B$.</h2>
<br>
<pre class="moz-signature" cols="72">--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: <a class="moz-txt-link-abbreviated" href="mailto:castorin@mat.uniroma2.it">castorin@mat.uniroma2.it</a>
tel: +390672594653</pre>
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