# Asymptotics of the $s$-fractional Gaussian perimeter as $s\to 0^+$

created by carbotti on 10 Jun 2021
modified on 15 Jun 2021

[BibTeX]

Submitted Paper

Inserted: 10 jun 2021
Last Updated: 15 jun 2021

Pages: 13
Year: 2021

ArXiv: 2106.05641 PDF

Abstract:

We study the asymptotic behaviour of the renormalised $s$-fractional Gaussian perimeter of a set $E$ inside a domain $\Omega$ 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.