Regularity of generating families of functions

Physics – Mathematical Physics

Scientific paper

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accepted in Journal of Geometric Mechanics

Scientific paper

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.

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