The Hilbert–Carathéodory Form for Parametric Multiple Integral Problems in the Calculus of Variations

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We define, and discuss some properties of, a form which bears a relation to the Carathéodory form for multiple integral problems in the calculus of variations similar to the relation that the Hilbert 1-form of Finsler geometry bears to the Poincaré–Cartan form for one-dimensional variational problems.

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