Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (4): 389-396.

• Articles • Previous Articles    

GENERALIZED DERIVATIVES OF A REGION FUNCTION AND ITS APPLICATIONS

He Chong   

  1. Chongqing Branch of ISTIC, Chongqing
  • Received:1986-02-20 Online:1987-04-18 Published:1987-04-18

Abstract: This paper is based on tome fundamental concepts in [7], Clarke’s generalized derivatives[1], as well as Lasotra’s and Strauss’ s definitions of differential D(x) of a multivalued ’function f(x)[6]. Thereby, the generalized derivatives of a region function f(x) is defined as
DF=∪∩{G(x)⊆B(R),∀x∈B(R);G(x)=Fx=F(x)}
The existence of the generalized derivatives of a region function F(x) is discussed; the necessary and sufficient conditions of existence of the Frechet generalized derivatives of such a function is established.

Key words: Bingham fluid flow, penalty, orthogonality projection, finite element

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