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Some fine properties of currents and applications to distributional Jacobians

Published online by Cambridge University Press:  12 July 2007

Camillo De Lellis
Affiliation:
Scuola Normale Superiore P.zza dei Cavalieri 7, 56100 Pisa, Italy (delellis@cibs.sns.it)

Abstract

We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim, and we prove a rectifiability criterion for flat currents of finite mass. We apply these tools to study the structure of the distributional Jacobians of functions in the space BnV, defined by Jerrard and Soner. We define the subspace of special functions of bounded higher variation and we prove a closure theorem.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2002

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