Geodesic
On the structure of ${\mathscr A}$-free measures and applications
Guido De Philippis1 ; Filip Rindler2
1 Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
2 Mathematics Institute, University of Warwick, Coventry, United Kingdom
Annals of mathematics, Tome 184 (2016) no. 3, pp. 1017-1039.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We establish a general structure theorem for the singular part of ${\mathscr A}$-free Radon measures, where ${\mathscr A}$ is a linear PDE operator. By applying the theorem to suitably chosen differential operators ${\mathscr A}$, we obtain a simple proof of Alberti’s rank-one theorem and, for the first time, its extensions to functions of bounded deformation (BD). We also prove a structure theorem for the singular part of a finite family of normal currents. The latter result implies that the Rademacher theorem on the differentiability of Lipschitz functions can hold only for absolutely continuous measures and that every top-dimensional Ambrosio–Kirchheim metric current in $\mathbb R^d$ is a Federer–Fleming flat chain.
DOI : 10.4007/annals.2016.184.3.10

Guido De Philippis 1 ; Filip Rindler 2

1 Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
2 Mathematics Institute, University of Warwick, Coventry, United Kingdom 
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Guido De Philippis; Filip Rindler. On the structure of ${\mathscr A}$-free measures and applications. Annals of mathematics, Tome 184 (2016) no. 3, pp. 1017-1039. doi : 10.4007/annals.2016.184.3.10. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.184.3.10/

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