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Regularity of generating families of functions

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  • We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions, under which a family of functions generates an immersed Lagrangian submanifold. These conditions are given in terms of the Hessian of the family.
    Mathematics Subject Classification: Primary: 53D12, 70G75; Secondary: 70H99, 49S05.


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