Gamma-convergence of fractional Gaussian perimeter

Abstract

We prove the $\Gamma$-convergence of the renormalised fractional Gaussian $s$-perimeter to the Gaussian perimeter as $s\to 1^{-}$. Our definition of fractional perimeter comes from that of the fractional powers of Ornstein-Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the $\Gamma$-limit does not depend on the dimension.

30 pages, 3 figures

References in corpus (1)

• Gamma-convergence of nonlocal perimeter functionals