The calculus of variations for multiple integrals depending on higher order derivatives
Annals of Global Analysis and Geometry (Impact Factor: 0.68). 02/1984; 2(1):19-54. DOI: 10.1007/BF01871944
.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
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