Asymptotics of the $s$-fractional Gaussian perimeter as $s\to 0^+$
Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara · arXiv (Cornell University) · 2021
We study the asymptotic behaviour of the renormalised $s$-fractional Gaussian perimeter of a set $E$ inside a domain $Ω$ as $s\to 0^+$. Contrary to the Euclidean case, as the Gaussian measure is finite, the shape of the set at infinity does not matter, but, surprisingly, the limit set function is never additive.