ASYMPTOTIC BEHAVIOR OF BV FUNCTIONS AND SETS OF FINITE PERIMETER IN METRIC MEASURE SPACES

doi:10.1090/tran/8495

CSpace > 应用数学研究所

	ASYMPTOTIC BEHAVIOR OF BV FUNCTIONS AND SETS OF FINITE PERIMETER IN METRIC MEASURE SPACES
	Eriksson-Bique, Sylvester 1; Gill, James T.2; Lahti, Panu3 ; Shanmugalingam, Nageswari 4
	2021-11-01
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	374 期号:11 页码:8201-8247
摘要	In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a 1-Poincare inequality. We show that at almost every point x outside the Cantor and jump parts of a BV function, the asymptotic limit of the function is a Lipschitz continuous function of least gradient on a tangent space to the metric space based at x. We also show that, at co-dimension 1 Hausdorff measure almost every measure-theoretic boundary point of a set E of finite perimeter, there is an asymptotic limit set (E)(infinity) corresponding to the asymptotic expansion of E and that every such asymptotic limit (E)(infinity) is a quasiminimal set of finite perimeter. We also show that the perimeter measure of (E)(infinity) is Ahlfors co-dimension 1 regular.
关键词	Bounded variation finite perimeter asymptotic limit doubling measure Poincare inequality least gradient function
DOI	10.1090/tran/8495
收录类别	SCI
语种	英语
资助项目	NSF[DMS-1704215] ; NSF[DMS-1500440] ; Finnish Cultural Foundation
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000710297900023
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59546
专题	应用数学研究所
通讯作者	Eriksson-Bique, Sylvester
作者单位	1.Res Unit Math Sci, POB 3000, FI-90014 Oulu, Finland 2.St Louis Univ, Dept Math & Stat, Ritter Hall 307,220 N Grand Blvd, St Louis, MO 63103 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Cincinnati, Dept Math Sci, POB 210025, Cincinnati, OH 45221 USA
推荐引用方式 GB/T 7714	Eriksson-Bique, Sylvester,Gill, James T.,Lahti, Panu,et al. ASYMPTOTIC BEHAVIOR OF BV FUNCTIONS AND SETS OF FINITE PERIMETER IN METRIC MEASURE SPACES[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2021,374(11):8201-8247.
APA	Eriksson-Bique, Sylvester,Gill, James T.,Lahti, Panu,&Shanmugalingam, Nageswari.(2021).ASYMPTOTIC BEHAVIOR OF BV FUNCTIONS AND SETS OF FINITE PERIMETER IN METRIC MEASURE SPACES.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,374(11),8201-8247.
MLA	Eriksson-Bique, Sylvester,et al."ASYMPTOTIC BEHAVIOR OF BV FUNCTIONS AND SETS OF FINITE PERIMETER IN METRIC MEASURE SPACES".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 374.11(2021):8201-8247.