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Some concepts of regularity for parametric multiple-integral problems in the calculus of variations. (English) Zbl 1224.58012
Summary: We show that asserting 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-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter \((m+1)\)-form are holonomic.

MSC:
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
49N60 Regularity of solutions in optimal control
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