A. Carbotti - S. Cito - D. A. La Manna - D. Pallara
Asymptotics of the $s$-fractional Gaussian perimeter as $s\to 0^+$
Published Paper
Inserted: 10 jun 2021
Last Updated: 22 aug 2022
Journal: Fractional Calculus and Applied Analysis
Pages: 13
Year: 2022
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.
Keywords: fractional Sobolev spaces, Fractional perimeters, Gaussian analysis, Fractional Ornstein-Uhlenbeck operator
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