A geometrical theory of multiple integral problems in the calculus of variations

1971 ◽  
Vol 7 (2-3) ◽  
pp. 173-181 ◽  
Author(s):  
E. T. Davies
Keyword(s):  
Calculus Of Variations ◽  
Multiple Integral ◽  
Geometrical Theory

A Geometrical Theory of Multiple Integral Problems in the Calculus of Variations

1968 ◽  
Vol 20 ◽  
pp. 639-657 ◽  
Author(s):  
H. Rund
Keyword(s):  
Calculus Of Variations ◽  
Multiple Integral ◽  
Dimensional Subspace ◽  
Geometrical Theory ◽  
Local Coordinates ◽  
Image Position

Let Xn denote an n-dimensional differentiate manifold referred to local coordinates xi. An m-dimensional subspace Cm (m < n) of Xn can be represented parametrically in the form1.1

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