Complex associated to some systems of PDE

Bonneau, Pierre; Mazzilli, Emmanuel

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.geomphys.2021.104319

Title :

Complex associated to some systems of PDE

Author(s) :

Bonneau, Pierre [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Mazzilli, Emmanuel [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Geometry and Physics

Pages :

28 pages.

Publisher :

Elsevier

Publication date :

2021

ISSN :

0393-0440

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In this paper, we construct the complex associated to an overdetermined system of PDE of order one with constant coefficients using the theory of exterior differential system of Cartan (see [1]). We show that if the tableau ...
Show more >In this paper, we construct the complex associated to an overdetermined system of PDE of order one with constant coefficients using the theory of exterior differential system of Cartan (see [1]). We show that if the tableau associated to the system of PDE is in involution then the complex contains only operators of order one given by the successive torsions of the system (see section 2 for the details). Moreover in section 3, we give a simple direct proof of “the involution of tableau” by prolongation process in this particular case (theorem of Cartan-Kuranishi in this context). Finally in the last section, we construct the complex associated to the Cauchy-Fueter operator (in fact, more general system of PDE containing Cauchy-Fueter equations) using the previous results. We can note that the system of PDE associated to the Cauchy-Fueter operator is not in involution contrarily of the De Rham or Dolbeault operators (this complex was first constructed by [5] by using computer algebra methods, and by [6] and [7] with the help of theory of Leray's spectral sequence). We can add that the key point to obtain many of the above results is a useful characterization of the involution of a tableau given in section 2.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :