Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$
Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara · Fractional Calculus and Applied Analysis · 2022
Abstract We study the asymptotic behaviour of the renormaliseds-fractional Gaussian perimeter of a setEinside a domain $$\Omega $$ Ω as $$s\rightarrow 0^+$$ s→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.