Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Cito - D. A. La Manna - D. Pallara

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

created by carbotti on 10 Jun 2021
modified on 22 Aug 2022


Published Paper

Inserted: 10 jun 2021
Last Updated: 22 aug 2022

Journal: Fractional Calculus and Applied Analysis
Pages: 13
Year: 2022

ArXiv: 2106.05641 PDF


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.

Keywords: fractional Sobolev spaces, Fractional perimeters, Gaussian analysis, Fractional Ornstein-Uhlenbeck operator