Comptes Rendus
no. 17-18
Partial Differential Equations
An extension of the identity Det=det
[Une extension de l'identité Det=det]

Présenté par : John Ball

Camillo De Lellis1 ; Francesco Ghiraldin2
1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Scuola Normale Superiore, P.zza dei Cavalieri, 7, 56126 Pisa, Italy
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 973-976.

Dans cette Note on étudie la caractérisation ponctuelle du jacobien des applications BnV au sens des distributions. On étend un résultat bien connu de Müller à une classe plus naturelle de fonctions, en utilisant le théorème de la divergence pour écrire le jacobien comme une intégrale de contour.

In this Note we study the pointwise characterization of the distributional Jacobian of BnV maps. After recalling some basic notions, we will extend the well-known result of Müller to a more natural class of functions, using the divergence theorem to express the Jacobian as a boundary integral.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.07.019
Camillo De Lellis 1 ; Francesco Ghiraldin 2

1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
2 Scuola Normale Superiore, P.zza dei Cavalieri, 7, 56126 Pisa, Italy 
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Camillo De Lellis; Francesco Ghiraldin. An extension of the identity $ \mathbf{Det}=\mathbf{det}$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 973-976. doi : 10.1016/j.crma.2010.07.019. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.019/

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