Recent trends in Geometric analysis and applications

Convergence of the s-perimeter and its gradient flow as $s \to 0$

speaker: Matteo Novaga (Unversità di Pisa)

abstract: I will present a unified point of view on fractional perimeters and Riesz potentials. Denoting by $H^s$ - for $s \in (0, 1)$ - the $s$-fractional perimeter and by $J^s$ - for $s \in (-d, 0)$ - the $s$-Riesz energies acting on characteristic functions, I will show that the functionals $H^s$ and $J^s$, up to a suitable additive renormalization diverging when $s \to 0$, belong to a continuous one-parameter family of functionals, which for $s = 0$ gives back a new object we refer to as $0$-fractional perimeter. All the convergence results are obtained in the framework of $\Gamma$-convergence. I will also discuss the convergence of the fractional mean curvature flow as $s\to 0$.

These results are in collaboration with A. Cesaroni, L. De Luca and M. Ponsiglione.

timetable:
Tue 26 Nov, 10:30 - 11:20, Aula Dini
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