Trivial Second-Order Lagrangians in Classial Field Theory

Trivial second-order Lagrangians are studied and a complete description of the dependence on the second-order derivatives is given. This extends previous work of Olver and others. In particular, this description involves some polynomial expressions called hyper-Jacobians. There exists some linear dependencies between these polynomials which are elucidated for the (second-order) hyper-Jacobians.