BMO-Type Norms Related to the Perimeter of Sets

被引：28

作者：

Ambrosio, Luigi ^{[1
]}

Bourgain, Jean ^{[2
]}

Brezis, Haim ^{[3
,4
]}

Figalli, Alessio ^{[5
]}

机构：

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56100 Pisa, Italy

[2] Inst Adv Study, Sch Math, Princeton, NJ 08540 USA

[3] Rutgers State Univ, Dept Math, Hill Ctr, Busch Campus,110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[4] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[5] Univ Texas Austin, Dept Math, 2515 Speedway Stop C1200, Austin, TX 78712 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2016年 / 69卷 / 06期

基金：

美国国家科学基金会;

关键词：

ISOPERIMETRIC INEQUALITY;

D O I：

10.1002/cpa.21620

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider an isotropic variant of the BMO-type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.(c) 2016 Wiley Periodicals, Inc.

引用

页码：1062 / 1086

页数：25

共 14 条

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