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Some fine properties of currents and applications to distributional Jacobians


De Lellis, C (2002). Some fine properties of currents and applications to distributional Jacobians. Proceedings of the Royal Society of Edinburgh: Section A, 132(4):815-842.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Royal Society of Edinburgh
ISSN:0308-2105
Publisher DOI:https://doi.org/10.1017/S030821050000189X
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1926918

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