Czechoslovak Mathematical Journal, Vol. 59, No. 3, pp. 741-758, 2009

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

M. Crampin, D. J. Saunders

M. Crampin, Address for correspondence: 65 Mount Pleasant, Aspley Guise, Beds MK17 8JX, UK, e-mail: Crampin@btinternet.com; Department of Mathematical Physics and Astronomy, Ghent University, Krijgslaan 281, B-9000 Gent, Belgium; D. J. Saunders, Department of Algebra and Geometry, Palacky University, 779 00 Olomouc, Czech Republic

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.

Keywords: parametric variational problem, regularity, multisymplectic

Classification (MSC 2000): 58E15, 49N60


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