Gamma-convergence of Gaussian fractional perimeter-Reference-Cited by-同舟云学术

Gamma-convergence of Gaussian fractional perimeter

Published:2021-12-02 Issue:0 Volume:0 Page:
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Carbotti Alessandro¹^ORCID,Cito Simone¹^ORCID,La Manna Domenico Angelo²^ORCID,Pallara Diego³^ORCID

Affiliation:

1. Dipartimento di Matematica e Fisica “E. De Giorgi” , Università del Salento , Via Per Arnesano, 73100 Lecce , Italy

2. Department of Mathematics and Statistics , University of Jyväskylä , P.O. Box 35 (MaD), FI-40014 , Jyväskylä , Finland

3. Dipartimento di Matematica e Fisica “E. De Giorgi” , Università del Salento ; and INFN, Sezione di Lecce, Via Per Arnesano, 73100 Lecce , Italy

Abstract

Abstract We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1 -

{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 Γ-limit does not depend on the dimension.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2021-0032/pdf

Reference33 articles.

1. G. Alberti and G. Bellettini, A non-local anisotropic model for phase transitions: Asymptotic behaviour of rescaled energies, European J. Appl. Math. 9 (1998), no. 3, 261–284.

2. L. Ambrosio, G. De Philippis and L. Martinazzi, Gamma-convergence of nonlocal perimeter functionals, Manuscripta Math. 134 (2011), no. 3–4, 377–403.

3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., The Clarendon, New York, 2000.

4. J. Berendsen and V. Pagliari, On the asymptotic behaviour of nonlocal perimeters, ESAIM Control Optim. Calc. Var. 25 (2019), Paper No. 48.

5. C. Borell, The Brunn–Minkowski inequality in Gauss space, Invent. Math. 30 (1975), no. 2, 207–216.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Cheeger problem in abstract measure spaces;Journal of the London Mathematical Society;2023-12-26

2. Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$;Fractional Calculus and Applied Analysis;2022-08