[CvGmt News] Seminario Eleonora Cinti (WIAS, Berlin) 19/4

[sorrenti at axp.mat.uniroma2.it]

SEMINARIO DI ANALISI ED EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Università degli Studi di Roma "Tor Vergata"



Martedi 19 Aprile 2016, ore 14:30, Aula dal Passo

Eleonora Cinti (WIAS, Berlino)

Quantitative flatness results and BV-estimates for nonlocal minimal surfaces.

Abstract:

We establish quantitative properties of minimizers and stable sets for
nonlocal interaction functionals, including the $s$-fractional perimeter
as a particular case. On the one hand, we establish universal BV-estimates
in every dimension $n\ge 2$ for stable sets. This nonlocal result is new
even in the case of $s$-perimeters and its local counterpart (for
classical stable minimal surfaces) was known, under some topological
assumptions, only in dimension $n=3$. On the other hand, we prove
quantitative flatness estimates for minimizers and stable sets in low
dimensions $n=2,3$. More precisely, we show that a stable set in $B_R$,
with $R$ large, is very close in measure to being a half space in $B_1$
--- with a quantitative estimate on the measure of the symmetric
difference. As a byproduct, we obtain new classification results for
stable sets in the whole plane.
This is a joint work with J. Serra and E. Valdinoci.



Website: http://www.mat.uniroma2.it/~castorin/Seminario-PDE.html