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arXiv · 2103.16598

Gamma-convergence of fractional Gaussian perimeter

Alessandro Carbotti·Simone Cito·Domenico Angelo La Manna·Diego Pallara
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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.

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Alessandro Carbotti, Simone Cito, Domenico Angelo La Manna, Diego Pallara. 2021-03-30. Gamma-convergence of fractional Gaussian perimeter. https://arxiv.org/abs/2103.16598

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