A Cauchy-Kowalevsky Theorem for Overdetermined Systems of Nonlinear Partial Differential Equations and Geometric Applications

被引：1

作者：

Baouendi, M. S. ^{[1
]}

Ebenfelt, P. ^{[1
]}

Zaitsev, D. ^{[2
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Trinity Coll Dublin, Sch Math, Dublin, Ireland

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 34卷 / 10期

基金：

爱尔兰科学基金会;

关键词：

Approximate solutions; Cauchy problem; Exterior differential systems; Finitely nondegenerate hypersurfaces; Levi number; Overdetermined systems; CR-MANIFOLDS; REAL;

D O I：

10.1080/03605300902910220

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a Cauchy problem for an overdetermined system of nonlinear partial differential equations, and give necessary and sufficient conditions for solvability of this Cauchy problem for all data. As an application, we find all real tube hypersurfaces in complex space whose Levi number is maximal.

引用

页码：1180 / 1207

页数：28

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