Resumen de Variational Characterization of Equations of Motion in Bundles of Embeddings.

Hernán Cendra , Ernesto A. Lacomba

• In this paper we study variational principles for a general situation which includes free boundary problems with surface tension. Following [2], our main result concerns a variational principle in a infinite dimensional principal bundle of embeddings of a compact region D in a manifold M having the same dimension as D. By considering arbitrary variations, free boundary problems are included, while variations parallel to the boundary permit to consider fluid motion or flow of Hamiltonian vector fields in non compact regions, generalizing [3], [4].

  In section 2 the main result is stated and proved. The Lagrangian includes a boundary term allowing us to include surface tension [5], or to remove it. Section 3 applies our result to Hamiltonian vector fields, while Section 4 concerns free boundary problems.