# [CvGmt News] seminario Cinti 15/5

Daniele Castorina castorin at mat.uniroma2.it
Wed May 8 12:55:22 CEST 2013

Cari amici,

vi segnalo il prossimo seminario di Equazioni Differenziali a Tor Vergata:

Martedi' 14 Maggio 2013, h 15:15, Aula Dal Passo

Eleonora Cinti - Università di Bologna

"Boundedness and regularity of isoperimetric sets with density"

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.

--
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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