4 papers
Asymptotic behaviour of rescaled nonlocal functionals and evolutions
Valerio Pagliari
Taking up a variational viewpoint, we present some nonlocal-to-local asymptotic results for various kinds of integral functionals. The content of the thesis comprises the contribut…
On the convergence rate of some nonlocal energies
Antonin Chambolle, Matteo Novaga, Valerio Pagliari
We study the rate of convergence of some nonlocal functionals recently considered by Bourgain, Brezis and Mironescu. In particular we establish the -convergence of the correspon…
Halfspaces minimise nonlocal perimeter: a proof via calibrations
Valerio Pagliari
We consider a nonlocal functional that may be regarded as a nonlocal version of the total variation. More precisely, for any measurable function $u\colon \mathbb{R}^d \to \ma…
On the asymptotic behaviour of nonlocal perimeters
Judith Berendsen, Valerio Pagliari
We study a class of integral functionals known as nonlocal perimeters, which, intuitively, express a weighted interaction between a set and its complement. The weight is provided b…