Canonical Cartan equations for higher order variational problems (Q1080240)

The problem of global variational calculus is to formulate intrinsically the Euler-Lagrange equations which characterize the critical sections. For variational problems of arbitrary order in one variable and for those in n-variables of order 1 or 2, this is attained by means of the Poincaré-Cartan form. The known result for r-order variational problems in n variables with \(r>2\) and \(n>1\) is that the Poincaré-Cartan form is not unique. The author of the present paper shows that there exists a unique ordinary \((n+1)\)-form which fulfills three simple axioms.