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Gamma-convergence of Gaussian fractional perimeter

  • Alessandro Carbotti ORCID logo , Simone Cito ORCID logo , Domenico Angelo La Manna ORCID logo EMAIL logo and Diego Pallara ORCID logo


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.

MSC 2010: 35R11; 49Q20

Communicated by Gianni Dal Maso

Funding statement: Alessandro Carbotti was partially supported by the TALISMAN project Cod. ARS01-01116. Simone Cito was partially supported by the ACROSS project Cod. ARS01-00702. Domenico Angelo La Manna was supported by the Academy of Finland grant 314227. Diego Pallara is member of G.N.A.M.P.A. of the Italian Istituto Nazionale di Alta Matematica (INdAM) and was partially supported by the PRIN 2015 MIUR project 2015233N54.


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Received: 2021-03-30
Accepted: 2021-08-19
Published Online: 2021-12-02
Published in Print: 2023-07-01

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