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Cari amici,<br>
<br>
vi segnalo il prossimo seminario di Equazioni Differenziali a Tor
Vergata:<br>
<br>
<h2><small>Martedi' 14 Maggio 2013, h 15:15, Aula Dal Passo
</small></h2>
<small>
</small>
<h2><small>Eleonora Cinti - Università di Bologna
</small></h2>
<small>
</small>
<h2><small>"Boundedness and regularity of isoperimetric sets with
density"<br>
<br>
We show that every isoperimetric set in $\R^N$with density is
bounded if the density is continuous and bounded by above and
below. This improves the previously known boundedness results,
which basically needed a Lipschitz assumption; on the other
hand, the present assumption is sharp, as we show with an
explicit example. To obtain our result, we observe that the main
tool which is often used, namely a classical
``$\epsilon-\epsilon$'' property already discussed by Allard,
Almgren and Bombieri, admits a weaker counterpart which is still
sufficient for the boundedness, namely, an
``$\epsilon-\epsilon^\beta$'' version of the property. And in
turn, while for the validity of the first property the Lipschitz
assumption is essential, for the latter the sole continuity is
enough. As consequences of the "$\epsilon-\epsilon^\beta$''
property, we derive some results about the existence and
regularity of isoperimetric sets. This is a joint work with Aldo
Pratelli. </small></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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