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.
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@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 -
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] Sobolev Spaces, Academic Press, 1975
[2] The fundamental theorem of surface theory with little regularity, J. Elasticity, Volume 73 (2003), pp. 251-290
[3] On Pfaff systems with coefficients and their applications in differential geometry, J. Math. Pures Appl., Volume 84 (2005), pp. 1659-1692
[4] On systems of first order linear partial differential equations with coefficients, Adv. Differential Equations, Volume 12 (2007), pp. 301-360
[5] Systems of total differential equations defined over simply connected domains, Ann. Math., Volume 35 (1934), pp. 730-734
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