Inserted: 10 jun 2021
Last Updated: 15 jun 2021
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