[CvGmt News] seminario Cinti 15/5

[Daniele Castorina]

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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