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Some geometric aspects of the calculus of variations in several independent variables. (English) Zbl 1235.58014
Summary: This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.

MSC:
58E30 Variational principles in infinite-dimensional spaces
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
49K10 Optimality conditions for free problems in two or more independent variables
35A15 Variational methods applied to PDEs
58A10 Differential forms in global analysis
58A20 Jets in global analysis
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References:
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