A brief history of the Jacobian

Haïm Brezis (1) , Jean Mawhin (2) , Petru Mironescu (3, 4)

1 Department of Mathematics - Rutgers School of Arts and Sciences
2 irmp - Institut de recherche en mathématique et physique
3 EDPA - Équations aux dérivées partielles, analyse
4 ICJ - Institut Camille Jordan

In his pioneering work, Jacobi discovered two remarkable identities related to the Jacobian. The first one asserts that the Jacobian has a divergence structure. The second one, that some vector fields involving the cofactors of the Jacobian are divergence free. We illustrate the fundamental impact of these properties on research, from the times of Jacobi to our days.

Mots clés: Distributional Jacobian; Divergence structure

Domaines: Mathématiques [math]

Haïm Brezis, Jean Mawhin, Petru Mironescu. A brief history of the Jacobian. Communications in Contemporary Mathematics, 2024, 26 (02), pp.Article 2330001. ⟨10.1142/S021919972330001X⟩. ⟨hal-04059234⟩