Comptes Rendus
Partial Differential Equations
An extension of the identity Det=det
[Une extension de l'identité Det=det]
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 :
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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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