Multi-brackets of differential operators and compatibility of PDE systems

Boris Kruglikov; Valentin Lychagin

doi:10.1016/j.crma.2006.02.013

Partial Differential Equations

Multi-brackets of differential operators and compatibility of PDE systems
[Multi-crochets d'opérateurs différentiels et compatibilité des systèms d'EDP]

Présenté par : Bernard Malgrange

Boris Kruglikov ¹ ; Valentin Lychagin ¹

¹ Institute of Mathematics and Statistics, University of Tromsø, Tromsø 9037, Norway

Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 557-561.

Résumé
Abstract

Nous établissons un critère de compatibilité efficace pour un système détérminé de type intersection complète généralisée en termes de multi-crochets.

We establish an efficient compatibility criterion for an overdetermined system of generalized complete intersection type in terms of multi-brackets.

Reçu le : 2005-09-06
Accepté le : 2006-02-07
Publié le : 2006-03-09

DOI : 10.1016/j.crma.2006.02.013

Affiliations des auteurs :

Boris Kruglikov ¹ ; Valentin Lychagin ¹

¹ Institute of Mathematics and Statistics, University of Tromsø, Tromsø 9037, Norway

@article{CRMATH_2006__342_8_557_0,
     author = {Boris Kruglikov and Valentin Lychagin},
     title = {Multi-brackets of differential operators and compatibility of {PDE} systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {557--561},
     publisher = {Elsevier},
     volume = {342},
     number = {8},
     year = {2006},
     doi = {10.1016/j.crma.2006.02.013},
     language = {en},
}

TY  - JOUR
AU  - Boris Kruglikov
AU  - Valentin Lychagin
TI  - Multi-brackets of differential operators and compatibility of PDE systems
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 557
EP  - 561
VL  - 342
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2006.02.013
LA  - en
ID  - CRMATH_2006__342_8_557_0
ER  -

%0 Journal Article
%A Boris Kruglikov
%A Valentin Lychagin
%T Multi-brackets of differential operators and compatibility of PDE systems
%J Comptes Rendus. Mathématique
%D 2006
%P 557-561
%V 342
%N 8
%I Elsevier
%R 10.1016/j.crma.2006.02.013
%G en
%F CRMATH_2006__342_8_557_0

Boris Kruglikov; Valentin Lychagin. Multi-brackets of differential operators and compatibility of PDE systems. Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 557-561. doi : 10.1016/j.crma.2006.02.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.013/

Bibliographie
Cité par

[1] W. Bruns; J. Herzog Cohen–Macaulay Rings, Cambridge University Press, Cambridge, UK, 1993

[2] D.A. Buchsbaum; D.S. Rim A generalized Koszul complex, II. Depth and multiplicity, Trans. Amer. Math. Soc., Volume 111 (1964), pp. 197-224

[3] H. Goldschmidt Integrability criteria for systems of nonlinear partial differential equations, J. Differential Geom., Volume 1 (1967) no. 3, pp. 269-307

[4] V. Guillemin; S. Sternberg An algebraic model of transitive differential geometry, Bull. Amer. Math. Soc., Volume 70 (1964), pp. 16-47

[5] I.S. Krasilschik; V.V. Lychagin; A.M. Vinogradov Geometry of Jet Spaces and Differential Equations, Gordon and Breach, 1986

[6] B.S. Kruglikov; V.V. Lychagin Mayer brackets and solvability of PDEs – I, Differential Geom. Appl., Volume 17 (2002), pp. 251-272

[7] B.S. Kruglikov; V.V. Lychagin Mayer brackets and solvability of PDEs – II, Trans. Amer. Math. Soc., Volume 358 (2006) no. 3, pp. 1077-1103 (article electronically published on April 22, 2005)

[8] B.S. Kruglikov; V.V. Lychagin A compatibility criterion for systems of PDEs and generalized Lagrange–Charpit method, Global Analysis and Applied Mathematics: International Workshop on Global Analysis, AIP Conf. Proc., vol. 729 (1), 2004, pp. 39-53

[9] S. Lie, F. Engel, Theorie der Transformationsgruppen, vol. II, Begründungstransformationen, Leipzig, Teubner, 1888–1893

[10] B. Malgrange Equations de Lie. I & II, J. Differential Geometry, Volume 6 (1972), pp. 503-522 (in French)

[11] D.C. Spencer Overdetermined systems of linear partial differential equations, Bull. Amer. Math. Soc., Volume 75 (1969), pp. 179-239

Cité par Sources :

Commentaires - Politique