On Pfaff systems with $ {L}^{p}$ coefficients in dimension two

Sorin Mardare

doi:10.1016/j.crma.2005.05.013

Partial Differential Equations

On Pfaff systems with

L^{p}

coefficients in dimension two
[Sur les systèmes de Pfaff en dimension deux]

Présenté par : Philippe G. Ciarlet

Sorin Mardare ¹

¹ Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France

Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 879-884.

Résumé
Abstract

On montre que le problème de Cauchy associé à un système de Pfaff avec des coefficients dans $L_{loc}^{p}$ , $p > 2$ , dans un ouvert connexe et simplement connexe Ω de $R^{2}$ admet une solution unique pourvu que ses coefficients satisfassent une condition de compatibilité au sens des distributions.

We prove that the Cauchy problem associated with a Pfaff system with coefficients in $L_{loc}^{p}$ , $p > 2$ , in a connected and simply-connected open subset Ω of $R^{2}$ has a unique solution provided that its coefficients satisfies a compatibility condition in the distributional sense.

Reçu le : 2005-04-27
Accepté le : 2005-05-04
Publié le : 2005-06-15

DOI : 10.1016/j.crma.2005.05.013

Affiliations des auteurs :

Sorin Mardare ¹

¹ Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 4, place Jussieu, 75005 Paris, France

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     title = {On {Pfaff} systems with $ {L}^{p}$ coefficients in dimension two},
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     pages = {879--884},
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     volume = {340},
     number = {12},
     year = {2005},
     doi = {10.1016/j.crma.2005.05.013},
     language = {en},
}

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Sorin Mardare. On Pfaff systems with $ {L}^{p}$ coefficients in dimension two. Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 879-884. doi : 10.1016/j.crma.2005.05.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.05.013/

Bibliographie
Cité par

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[3] P. Hartman; A. Wintner On the fundamental equations of differential geometry, Amer. J. Math., Volume 72 (1950), pp. 757-774

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

[5] S. Mardare, On Pfaff systems with $L^{p}$ -coefficients and their applications in differential geometry, J. Math. Pures Appl., in press

[6] L. Schwartz Analyse II : Calcul Différentiel et Equations Différentielles, Hermann, Paris, 1992

[7] 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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