Some concepts of regularity for parametric multiple-integral problems in the calculus of variations

Abstract

We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Caratheodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter (m + 1)-form are holonomic.