Geodesic
Jacobi's bound for systems of algebraic differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 151-166 
M. V. Kondrat'eva; A. V. Mikhalev; E. V. Pankratiev. Jacobi's bound for systems of algebraic differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 4, pp. 151-166. http://geodesic.mathdoc.fr/item/FPM_2008_14_4_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This review paper is devoted to the Jacobi bound for systems of partial differential polynomials. We prove the conjecture for the system of $n$ partial differential equations in $n$ differential variables which are independent over a prime differential ideal $\mathfrak p$. On the one hand, this generalizes our result about the Jacobi bound for ordinary differential polynomials independent over a prime differential ideal $\mathfrak p$ and, on the other hand, the result by Tomasovic, who proved the Jacobi bound for linear partial differential polynomials.

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