The Hilbert-Carathéodory form for parametric multiple integral problems in the calculus of variations (Q1810776)
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scientific article; zbMATH DE number 1924871
| Language | Label | Description | Also known as |
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| English | The Hilbert-Carathéodory form for parametric multiple integral problems in the calculus of variations |
scientific article; zbMATH DE number 1924871 |
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The Hilbert-Carathéodory form for parametric multiple integral problems in the calculus of variations (English)
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9 June 2003
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The Hilbert 1-form, emphasized by Chern in Finsler geometry, is a special case of the Poincaré-Cartan form of Lagrangian dynamics. One can accomplish this with just a homogeneity condition. The authors show that the Carathéodory form for multiple integral problems can also be specialized in a similar manner. The new Hilbert (called Hilbert-Carathéodory) form is used to derive the Euler-Lagrange equations.
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calculus of variations
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multiple integral problems
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Finsler geometry
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Hilbert form
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