Comptes Rendus
no. 9
Partial Differential Equations
On the resolution of Pfaff systems in dimension three
Philippe G. Ciarlet
Sorin Mardare1
1Institüt für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 565-570

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.03.029

Sorin Mardare  1

1 Institüt für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland 
Sorin Mardare. On the resolution of Pfaff systems in dimension three. Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 565-570. doi: 10.1016/j.crma.2007.03.029
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[1] R.A. Adams Sobolev Spaces, Academic Press, 1975

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

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

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

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

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