Calculus and Fine Properties of Functions of Bounded Variation on RCD Spaces

被引：5

作者：

Brena, Camillo ^{[1
]}

Gigli, Nicola ^{[2
]}

机构：

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy

[2] Scuola Int Super Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 01期

关键词：

RCD space; Bounded variation; Calculus rule; Fine property; METRIC-MEASURE-SPACES; LOCAL DIRICHLET SPACES; FINITE PERIMETER; RICCI CURVATURE; LIPSCHITZ FUNCTIONS; SOBOLEV SPACES; SETS; GEOMETRY;

D O I：

10.1007/s12220-023-01434-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the classical calculus rules satisfied by functions of bounded variation to the framework of RCD spaces. In the infinite dimensional setting, we are able to define an analogue of the distributional differential and, on finite dimensional spaces, we prove fine properties and suitable calculus rules, such as the Vol'pert chain rule for vector valued functions.

引用

页数：54

共 50 条

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