On Null Lagrangians
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D. J. Saunders
Abstract
We consider Lagrangians for parametric variational problems defined on velocity manifolds and show that a Lagrangian is null precisely when its shadow, a family of vector forms, is closed. We also show that a null Lagrangian can be recovered (to within a constant) from its shadow, and therefore that such a Lagrangian is (again to within a constant) a sum of determinants of total derivatives.
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Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Finite Mixed Sums wih Harmonic Terms
- Packing of ℝ2 by Crosses
- On the Integrality of the Elementary Symmetric Functions of 1, 1/3, . . . , 1/(2n − 1)
- Generalized Derivations as a Generalization of Jordan Homomorphisms Acting on Lie Ideals and Right Ideals
- Generalized Derivations on Lie Ideals and Power Values on Prime Rings
- On Monoids of Injective Partial Cofinite Selfmaps
- Extensions of Dynamic Inequalities of Hardy’s Type on Time Scales
- The Controlled Convergence Theorem for the Gap-Integral
- The Solvability of a Nonlocal Boundary Value Problem
- Oscillation Criteria for Third Order Differential Equations with Functional Arguments
- Asymptotic Behavior of Solutions of a Nonlinear Neutral Generalized Pantograph Equation with Impulses
- On Null Lagrangians
- Principal Eigenvalues for Systems of Schrödinger Equations Defined in the whole Space with Indefinite Weights
- Convergence of Series on Large Set of Indices
- On Approximation Properties of a New Type of Bernstein-Durrmeyer Operators
- Representation of Extendible Bilinear Forms
- Spectra and Fine Spectra of Lower Triangular Double-Band Matrices as Operators on Lp (1 ≤ p < ∞)
- Topological Fundamental Groups and Small Generated Coverings
- A Relation between two Kinds of Norms for Martingales
- Linearization Regions in Singular Weakly Nonlinear Regression Models with Constraints
- Parametric Equilibrium Problems Governed by Topologically Pseudomonotone Bifunctions
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