Calculus of Variations and Geometric Measure Theory

C. De Lellis

Some fine properties of currents and applications to distributional jacobians

created on 20 Nov 2000
modified by delellis on 03 May 2011


Published Paper

Inserted: 20 nov 2000
Last Updated: 3 may 2011

Journal: Proc. Roy. Soc. of Ed. A
Volume: 132A
Pages: 815-842
Year: 2000


We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim (see \href{http:/cvgmt.sns.itpapersambkir99a}{papersambkirch99a}) 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.

In particular we propose a decomposition for normal currents which provides, applied to BnV, an analogue of Ambrosio-De Giorgi decomposition of the derivative of BV functions. Hence we define the subspace of special functions of bounded higher variation and we prove a closure theorem for it.

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