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.
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.
Accepted:
Published online:
Camillo De Lellis 1; Francesco Ghiraldin 2
@article{CRMATH_2010__348_17-18_973_0, author = {Camillo De Lellis and Francesco Ghiraldin}, title = {An extension of the identity $ \mathbf{Det}=\mathbf{det}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {973--976}, publisher = {Elsevier}, volume = {348}, number = {17-18}, year = {2010}, doi = {10.1016/j.crma.2010.07.019}, language = {en}, }
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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