Generalized convex functionals
نویسنده
چکیده
This paper studies functionals defined by multiple integrals associated to differential forms on the jet bundle of first order corresponding to some Riemannian manifolds; the domain of these functionals consists in submanifold maps satisfying certain conditions of integrability. Our idea is to give geometric properties to the domain of a functional allowing us to properly define convexity. The method we use consists in creating an extended Riemannian submanifold of the first order jet bundle, in connection to this domain and carrying back its geometric properties. This process allows us to consider and use the geodesic deformations. Furthermore, fixing a pairing map, allows us to define generalized convex (preinvex and invex) functionals. M.S.C. 2010: 52A20, 52A41, 53C21.
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