KMS Of Academy of mathematics and systems sciences, CAS
FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES | |
Lahti, Panu | |
2020 | |
Source Publication | ANALYSIS & PDE |
ISSN | 1948-206X |
Volume | 13Issue:5Pages:1501-1519 |
Abstract | Federer's characterization of sets of finite perimeter states (in Euclidean spaces) that a set is of finite perimeter if and only if the measure-theoretic boundary of the set has finite Hausdorff measure of codimension 1. In complete metric spaces that are equipped with a doubling measure and support a Poincare inequality, the "only if" direction was shown by Ambrosio (2002). By applying fine potential theory in the case p = 1, we prove that the "if" direction holds as well. |
Keyword | metric measure space set of finite perimeter Federer's characterization measure-theoretic boundary codimension-1 Hausdorff measure fine topology |
DOI | 10.2140/apde.2020.13.1501 |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000555886800007 |
Publisher | MATHEMATICAL SCIENCE PUBL |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51968 |
Collection | 应用数学研究所 |
Corresponding Author | Lahti, Panu |
Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
Recommended Citation GB/T 7714 | Lahti, Panu. FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES[J]. ANALYSIS & PDE,2020,13(5):1501-1519. |
APA | Lahti, Panu.(2020).FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES.ANALYSIS & PDE,13(5),1501-1519. |
MLA | Lahti, Panu."FEDERER'S CHARACTERIZATION OF SETS OF FINITE PERIMETER IN METRIC SPACES".ANALYSIS & PDE 13.5(2020):1501-1519. |
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