The calculus of variations for multiple integrals depending on higher order derivatives
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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ABSTRACT: The global formulation of the higher-order Poincar-Cartan form for Lagrangian field theories in the calculus of variations is re-examined in terms of the theory of lifts of tensor fields on a manifold to its higher-order prolongated jet bundles.Letters in Mathematical Physics 10/1987; 14(4):353-362. DOI:10.1007/BF00402145 · 1.94 Impact Factor