no. 9
Partial Differential Equations
On the resolution of Pfaff systems in dimension three
[Sur la résolution des systèmes de Pfaff en dimension trois]

Présenté par : Philippe G. Ciarlet

Mardare, Sorin1
1 Institüt für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
Comptes Rendus. Mathématique, Tome 344 (2007) no. 9, pp. 565-570.

On établit que le problème de Cauchy associé à un système de Pfaff en dimension trois a une solution unique sous des hypothèses minimales de régularité sur ses coefficients.

We establish that the Cauchy problem associated with a Pfaff system in dimension three has a unique solution under minimal regularity assumptions on its coefficients.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.03.029
Mardare, Sorin 1

1 Institüt für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland 
@article{CRMATH_2007__344_9_565_0,
     author = {Mardare, Sorin},
     title = {On the resolution of {Pfaff} systems in dimension three},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {565--570},
     publisher = {Elsevier},
     volume = {344},
     number = {9},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.029},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.03.029/}
}
TY  - JOUR
AU  - Mardare, Sorin
TI  - On the resolution of Pfaff systems in dimension three
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 565
EP  - 570
VL  - 344
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.03.029/
DO  - 10.1016/j.crma.2007.03.029
LA  - en
ID  - CRMATH_2007__344_9_565_0
ER  - 
%0 Journal Article
%A Mardare, Sorin
%T On the resolution of Pfaff systems in dimension three
%J Comptes Rendus. Mathématique
%D 2007
%P 565-570
%V 344
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.03.029/
%R 10.1016/j.crma.2007.03.029
%G en
%F CRMATH_2007__344_9_565_0
Mardare, Sorin. On the resolution of Pfaff systems in dimension three. Comptes Rendus. Mathématique, Tome 344 (2007) no. 9, pp. 565-570. doi : 10.1016/j.crma.2007.03.029. http://www.numdam.org/articles/10.1016/j.crma.2007.03.029/

[1] Adams, R.A. Sobolev Spaces, Academic Press, 1975

[2] Mardare, S. The fundamental theorem of surface theory with little regularity, J. Elasticity, Volume 73 (2003), pp. 251-290

[3] Mardare, S. On Pfaff systems with Lp coefficients and their applications in differential geometry, J. Math. Pures Appl., Volume 84 (2005), pp. 1659-1692

[4] Mardare, S. On systems of first order linear partial differential equations with Lp coefficients, Adv. Differential Equations, Volume 12 (2007), pp. 301-360

[5] Thomas, T.Y. Systems of total differential equations defined over simply connected domains, Ann. Math., Volume 35 (1934), pp. 730-734

Cité par Sources :