Geodesic
On Bi-dimensional Second Variation
Commentationes Mathematicae, Tome 52 (2012) no. 1, pp. 39-59.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this paper we present the concept of bounded second variation of a real valued function defined on a rectangle in \(\mathbb{R}^2\). We use Hardy-Vitali type technics in the plane in order to extend the classical notion of function of bounded second variation on intervals of \(\mathbb{R}\). We introduce the class \(BV^2(I_a^b )\), of all functions of bounded second variation on a rectangle \(I_a^b \subset \mathbb{R}^2\), and show that this class can be equipped with a norm with respect to which it is a Banach space. Finally, we present two results that show that integrals of functions of first bounded variation (on \(I_a^b\)) are in \(BV^2 (I_a^b)\).
DOI : 10.14708/cm.v52i1.5326
Mots-clés : Functions of Bounded Second Variation, Functions of Bounded Variation 
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Jurancy Ereú; José Giménez; Nelson Merentes. On Bi-dimensional Second Variation. Commentationes Mathematicae, Tome 52 (2012) no. 1, pp.  39-59. doi : 10.14708/cm.v52i1.5326. http://geodesic.mathdoc.fr/articles/10.14708/cm.v52i1.5326/

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