The calculus of variations for multiple integrals depending on higher order derivatives

Annals of Global Analysis and Geometry (Impact Factor: 0.79). 02/1984; 2(1):19-54. DOI: 10.1007/BF01871944

ABSTRACT .The formulation of the calculus of variations in the geometric version for the case of multiple integrals depen~ding on higher order derivatives is proposed. It generalizes the Lepage-Dedecker theory of variational problems with first derivatives. A notion of a geodesic field, an important tool to obtain sufficient conditions for extrema, is introduced and studied. General considerations are illustrated by an important example of a rigid plate.

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