6 papers · 1 filter
Local Density of Solutions to Fractional Equations
Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci
The study of nonlocal operators of fractional type possesses a long tradition, motivated both by mathematical curiosity and by real world applications...
Asymptotics of the -fractional Gaussian perimeter as
Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna +1
We study the asymptotic behaviour of the renormalised -fractional Gaussian perimeter of a set inside a domain as . Contrary to the Euclidean case, as the Gauss…
Gamma-convergence of fractional Gaussian perimeter
Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna +1
We prove the -convergence of the renormalised fractional Gaussian -perimeter to the Gaussian perimeter as . Our definition of fractional perimeter comes from that o…
Local minimizers and Gamma-convergence for nonlocal perimeters in Carnot Groups
Alessandro Carbotti, Sebastiano Don, Diego Pallara +1
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in…
Local density of Caputo-stationary functions of any order
Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci
We show that any given function can be approximated with arbitrary precision by solutions of linear, time-fractional equations of any prescribed order. This extends a recent result…
Local density of solutions of time and space fractional equations
Alessandro Carbotti, Serena Dipierro, Enrico Valdinoci
We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in whic…