The nonparametric Weierstrass integral over a BV curve as a length functional
type: Item
instance of: scholarly article
title: The nonparametric Weierstrass integral over a BV curve as a length functional
zbMATH Open document ID: 1018.49030
author: Loris Faina
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-08-24T00:00:00Z
review text: Following the outline of Menger's conjecture [\textit{K. Menger}, ``Géométrie générale'', Mém. Sci. Math. (1954; Zbl 0055.16001)] the author proves that the nonparametric Weierstrass integral over a BV curve [\textit{P. Brandi} and \textit{A. Salvadori}, ``On the definition and properties of a variational integral over a BV curve'', Rapporto Tecnico Dip. Math. Univ. Perugia (1988), ``On the non-parametric integral over a BV surface'', Nonlinear Anal., Theory Methods Appl. 13, 1127-1137 (1989; Zbl 0694.49029)] is a length with respect to a suitable metric. The parametric case was considered by the same author in ``The parametric Weierstrass integral over a BV curve as a length functional'' [Stud. Math. 127, 9-19 (1998; Zbl 0906.49020)].
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 49J10
zbMATH DE Number: 1441389
zbMATH Keywords: Weierstrass integral
zbMATH Keywords: function of bounded variation
zbMATH Keywords: length functional
reviewed by: Anna Salvadori
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6691
OpenAlex ID: W2020033345
cites work: Q4193688
cites work: Q4097792
cites work: Burkill-Cesari integrals of quasi additive interval functions
cites work: Q3866334
cites work: Q3911021
cites work: Q3888063
cites work: Sull'estensione dell'integrale debole alla Burkill-Cesari ad una misura
cites work: Q4720308
cites work: The nonparametric integral of the calculus of variations as a Weierstrass integral: existence and representation
cites work: Q3787031
cites work: On the lower semicontinuity of certain integrals of the calculus of variations
cites work: A quasi-additivity type condition and the integral over a BV variety
cites work: Q3983443
cites work: Quasi Additive Set Functions and the Concept of Integral Over a Variety
cites work: Extension Problem for Quasi Additive Set Functions and Radon-Nikodym Derivatives
cites work: The parametric Weierstrass integral over a BV curve as a length functional
cites work: Q5826272
cites work: Sulla convergenza in lunghezza in senso generalizzato con peso per una successione di curve parametriche
cites work: Q5513372
cites work: Q5562115
cites work: The Burkill-Cesari integral
DOI: 10.1006/JMAA.1999.6691
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description: scientific article; zbMATH DE number 1441389