scholarly journals Some existence theorems in the calculus of variations. IV. Isoperimetric problems in non-parametric form

1939 ◽  
Vol 45 (2) ◽  
pp. 173-173
Author(s):  
E. J. McShane
Keyword(s):  
Calculus Of Variations ◽  
Existence Theorems ◽  
Parametric Form ◽  
Isoperimetric Problems ◽  
Non Parametric

Isoperimetric Problems in the Calculus of Variations

1952 ◽  
Vol 4 ◽  
pp. 257-280 ◽  
Author(s):  
William Karush
Keyword(s):  
Calculus Of Variations ◽  
Classical Theory ◽  
Indirect Method ◽  
Direct Method ◽  
Isoperimetric Problems ◽  
End Points ◽  
Sufficiency Theorems ◽  
Theory Of Fields ◽  
A Direct Method ◽  
Problem Of Bolza

We are concerned with establishing sufficiency theorems for minima of simple integrals of the parametric type in a class of curves with variable end points and satisfying isoperimetric side conditions. The results which are obtained involve no explicit assumptions of normality. Such results can be derived by transforming our problem to a problem of Bolza and using the latest developments in the theory of that problem. More recently [6] an indirect method of proof has been published. Our object is to present a direct method of proof without transformation of the problem which is based upon a generalization of the classical theory of fields.

Sign in / Sign up

Export Citation Format

Share Document