ASYMPTOTIC BEHAVIOR OF BV FUNCTIONS AND SETS OF FINITE PERIMETER IN METRIC MEASURE SPACES
文献类型：期刊论文
| 作者 | Eriksson-Bique, Sylvester1; Gill, James T.2; Lahti, Panu3 ; Shanmugalingam, Nageswari4
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| 刊名 | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
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| 出版日期 | 2021-11-01 |
| 卷号 | 374期号:11页码:8201-8247 |
| 关键词 | Bounded variation finite perimeter asymptotic limit doubling measure Poincare inequality least gradient function |
| ISSN号 | 0002-9947 |
| DOI | 10.1090/tran/8495 |
| 英文摘要 | 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. |
| 资助项目 | NSF[DMS-1704215] ; NSF[DMS-1500440] ; Finnish Cultural Foundation |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000710297900023 |
| 出版者 | AMER MATHEMATICAL SOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59545]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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