A semigroup version of the isoperimetric inequality

被引：17

作者：

Preunkert, M ^{[1
]}

机构：

[1] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

来源：

SEMIGROUP FORUM | 2004年 / 68卷 / 02期

关键词：

heat semigroup; isoperimetric inequality; Caccioppoli sets;

D O I：

10.1007/s00233-003-0004-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we extend the heat semigroup version of the isoperimetric inequality in R-n established by M. Ledoux [6]. To this purpose, the notion of the perimeter of a Caccioppoli set introduced by E. De Giorgi [4] yields the appropriate measure theoretical background. In the proofs we use properties of the heat semigroup as well as its explicit integral representation.

引用

页码：233 / 245

页数：13

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[2]

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[3]

DE GIORGI E, 1953, ATTI ACAD NAZ L SFMN, V14, P390

[4]

Evans L. C., 2018, Measure Theory and Fine Properties of Functions

[5]

Giusti E., 1984, MINIMAL SURFACES FUN

[6]

LEDOUX M, 1994, B SCI MATH, V118, P485

[7] ISOPERIMETRIC INEQUALITY [J].

OSSERMAN, R .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 84 (06) :1182-1238

[8]

ZIEMER W, 1989, WEAKLY DIFFERENTIABL

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