On the resolution of Pfaff systems in dimension three

Sorin Mardare

doi:10.1016/j.crma.2007.03.029

Partial Differential Equations

On the resolution of Pfaff systems in dimension three

Presented by: Philippe G. Ciarlet

Sorin Mardare ¹

¹ Institüt für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

Comptes Rendus. Mathématique, Volume 344 (2007) no. 9, pp. 565-570.

Abstract
Résumé

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: 2007-03-07
Accepted: 2007-03-17
Published online: 2007-05-01

DOI: 10.1016/j.crma.2007.03.029

Author's affiliations:

Sorin Mardare ¹

¹ Institüt für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

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     title = {On the resolution of {Pfaff} systems in dimension three},
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     doi = {10.1016/j.crma.2007.03.029},
     language = {en},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.029/

References
Cited by

[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 $L^{p}$ 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 $L^{p}$ 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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