Calculus of Variations and Geometric Measure Theory

C. De Lellis

A note on Alberti's Rank--one Theorem

created by delellis on 30 Mar 2006
modified on 03 May 2011


Published Paper

Inserted: 30 mar 2006
Last Updated: 3 may 2011

Journal: Transport equations and multi-D hyperbolic conservation laws, 61-74, Lect. Notes Unione Mat. Ital., 5, Springer, Berlin..
Year: 2008


In this note we illustrate the original proof of the Alberti's Rank--one Theorem: If $u$ is a $BV$ map and $M
D^s u
$ the Radon--Nykodim decomposition of the singular part of $Du$, then $M (x)$ has rank $1$ for $
D^s u
$--almost every $x$.

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