Gamma-convergence of Gaussian fractions perimeter

被引：2

作者：

Carbotti, Alessandro ^{[2
]}

Cito, Simone ^{[2
]}

La Manna, Domenico Angelo ^{[1
]}

Pallara, Diego ^{[2
,3
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, FI-40014 Jyvaskyla, Finland

[2] Univ Salento, Dipartimento Matemat & Fis E De Giorgi, Via Per Arnesano, I-73100 Lecce, Italy

[3] Ist Nazl Fis Nucl, Sez Lecce, Via Per Arnesano, I-73100 Lecce, Italy

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2023年 / 16卷 / 03期

基金：

芬兰科学院;

关键词：

Fractional perimeters; Gaussian analysis; Gamma-convergence; EXTENSION PROBLEM; INEQUALITY; CONNECTIONS;

D O I：

10.1515/acv-2021-0032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the Gamma-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 Gamma-limit does not depend on the dimension.

引用

页码：571 / 595

页数：25

共 37 条

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[37] Asymptotics of the s-fractional Gaussian perimeter as s→0+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s\rightarrow 0^+$$\end{document}
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