On Pfaff systems with LP coefficients and their applications in differential geometry

被引：41

作者：

Mardare, S ^{[1
]}

机构：

[1] Univ Paris 06, Lab Jacques Louis Lions, F-75252 Paris, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2005年 / 84卷 / 12期

关键词：

Pfaffian system; stability; fundamental theorem of surface theory;

D O I：

10.1016/j.matpur.2005.08.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a Pfaff system with coefficients in L-loc(p), p > 2, in a simply-connected open subset to ohm of R-2 has at least a nontrivial solution of class W-loc(1,p)(ohm) provided that its coefficients satisfies a compatibility condition in the distributional sense. If in addition the set ohm is connected, the Cauchy problem associated with the Pfaff system has a unique solution. An application of this result is that the fundamental theorem of surface theory holds under the assumption that the first and second fundamental forms are respectively of class W-loc(1,p) and L-loc(p), with p > 2, and satisfy together the Gauss and Codazzi-Mainardi equations in the distributional sense. (c) 2005 Elsevier SAS. All rights reserved.

引用

页码：1659 / 1692

页数：34

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