Calculus of Variations and Geometric Measure Theory

Limiting behaviour of rescaled nonlocal perimeters and of their first variations

Valerio Pagliari (Institute of Analysis and Scientific Computing, TU Vienna)

created by gelli on 15 Mar 2018
modified on 28 Mar 2018

11 apr 2018 -- 17:00   [open in google calendar]

Sala Seminari Dipartimento di Matematica di Pisa


We introduce a class of integral functionals known as nonlocal perimeters, which can be thought as interactions between a set and its complement that are weighted by a positive kernel. In the first part of the talk, we summarise the main features of these functionals and then we study the asymptotic behaviour of the family associated with mass-preserving rescalings of a given kernel. Namely, we prove that when the scaling parameter approaches $0$, the rescaled non local perimeters $Gamma$-converge to De Giorgi's perimeter, up to a multiplicative constant. In the second part of the talk, we show that a similar result holds for nonlocal curvatures, i.e. for the first variations of the nonlocal perimeters; time permitting, we shall hint at possible applications of this to dislocation dynamics.