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Article

Crampin, M. ; Saunders, D. J.
Some concepts of regularity for parametric multiple-integral problems in the calculus of variations. (English). Czechoslovak Mathematical Journal, vol. 59 (2009), issue 3, pp. 741-758
MSC: 37Jxx, 49K10, 49N60, 53Cxx, 58E15, 70Gxx | MR 2545653 | Zbl 1224.58012
Keywords:
parametric variational problem; regularity; multisymplectic
Summary:
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-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter $(m+1)$-form are holonomic.
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