Lipschitz泛函的本质临界点

The Essenthally Critical Points of Lipschitz Functchionals

中文关键词:  Ranach空间  Lipschitz流形  Lipschitz泛函  临界点．

中文摘要:

      本文指出Ｂａｎａｃｈ空间中Ｃ^1－0（即局部Ｌｉｐｓｃｈｉｔｚ）泛函的Ｃｌａｒｋｅ－临界点一般不具有在Ｃ^1－0局部坐标变换下的不变性。据此提出了Ｃ^1－0泛函的本质临界点的概念，它能适应研究Ｃ^1－0流形上的Ｃ^1－0泛函的临界点的需要．还给出了有关本质临界点的几个结果。

英文摘要:

      We show that,in general,Clarke critical points of C^1－0 (i.e,locally Lipschitz) function-als in Banach spaces do not possess the invariance property under C^1－0 local coordinatetransformations. We then introduce the concept of the essentially critical points of C^1－0 functionals,which can be used to study C^1－0 functions on C^1－0 manifolds.We obtainsome results related to the essentially critical points.