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

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.

13 pages

References in corpus (1)

• Gamma-convergence of nonlocal perimeter functionals