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On necessary conditions in the calculus of variations. (English) Zbl 0946.49014

The paper considers the general isoperimetric problem with both equality and inequality constraints. The main results of the paper are Theorems 1 and 2 which give necessary conditions for weak and strong local solutions, respectively. Necessary conditions are obtained without the assumption that the integrands have partial derivatives in the phase variable, which is of interest since those derivatives do not appear in the corresponding Euler equation.

MSC:

49K05 Optimality conditions for free problems in one independent variable
49K10 Optimality conditions for free problems in two or more independent variables
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