Gamma-convergence for the fractional Gaussian perimeter

Abstract:

We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 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 Γ-limit does not depend on the dimension. This is a joint work with S. Cito, D. A. La Manna and D. Pallara.

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