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

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dc.contributor University of Helsinki, Department of Mathematics and Statistics en Exnerova, Vendula Honzlova Maly, Jan Martio, Olli 2020-11-30T23:25:59Z 2021-07-26T02:45:31Z 2018-12
dc.identifier.citation 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 . en
dc.identifier.issn 0362-546X
dc.identifier.other PURE: 119095108
dc.identifier.other PURE UUID: d674b649-af8c-4485-8a54-596080a5c787
dc.identifier.other WOS: 000449073400012
dc.identifier.other Scopus: 85049353781
dc.description.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. en
dc.format.extent 19
dc.language.iso eng
dc.relation.ispartof Nonlinear Analysis: Theory, Methods & Applications
dc.rights en
dc.subject Modulus of path family en
dc.subject Functions of bounded variation en
dc.subject EQUIVALENCE en
dc.subject 111 Mathematics en
dc.title Functions of bounded variation and the AM-modulus in R-n en
dc.type Article
dc.description.version Peer reviewed
dc.type.uri info:eu-repo/semantics/other
dc.type.uri info:eu-repo/semantics/acceptedVersion

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