Functions of bounded variation and the AM-modulus in R-n

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Exnerova , V H , Maly , J & Martio , O 2018 , ' Functions of bounded variation and the AM-modulus in R-n ' , Nonlinear Analysis: Theory, Methods & Applications , vol. 177 , pp. 553-571 .

Title: Functions of bounded variation and the AM-modulus in R-n
Author: Exnerova, Vendula Honzlova; Maly, Jan; Martio, Olli
Contributor organization: Department of Mathematics and Statistics
Date: 2018-12
Language: eng
Number of pages: 19
Belongs to series: Nonlinear Analysis: Theory, Methods & Applications
ISSN: 0362-546X
Abstract: Moduli of path families are widely used to study Sobolev functions. Similarly, the recently introduced approximation (AM-) modulus is helpful in the theory of functions of bounded variation (BV) in R-n (Martio, 2016). We continue this direction of research. Let Gamma(E) be the family of all paths which meet E subset of R-n. We introduce the outer measure E bar right arrow AM(Gamma(E)) and compare it with other (n - 1)-dimensional measures. In particular, we show that AM(Gamma(E)) = 2H(n-1)(Gamma(E)) whenever E lies on a countably (n - 1)-rectifiable set. Further, we study functions which have bounded variation on AM-a.e. path and we relate these functions to the classical BV functions which have only bounded essential variation on AM-a.e. path. We also characterize sets E of finite perimeter in terms of the AM-modulus of two path families naturally associated with E. (C) 2018 Elsevier Ltd. All rights reserved.
Subject: Modulus of path family
Functions of bounded variation
111 Mathematics
Peer reviewed: Yes
Rights: cc_by_nc_nd
Usage restriction: openAccess
Self-archived version: acceptedVersion

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