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 (Original language)
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

@article{CRMATH_2007__344_9_565_0,
     author = {Sorin Mardare},
     title = {On the resolution of {Pfaff} systems in dimension three},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {565--570},
     year = {2007},
     publisher = {Elsevier},
     volume = {344},
     number = {9},
     doi = {10.1016/j.crma.2007.03.029},
     language = {en},
}

TY  - JOUR
AU  - Sorin Mardare
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
DO  - 10.1016/j.crma.2007.03.029
LA  - en
ID  - CRMATH_2007__344_9_565_0
ER  -

%0 Journal Article
%A Sorin Mardare
%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
%R 10.1016/j.crma.2007.03.029
%G en
%F CRMATH_2007__344_9_565_0

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

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

Cited by Sources:

Comments - Policy