Abstract
We prove that, under the condition of nontriviality, the Euler-Lagrange and Noether equations are equivalent for a general class of scalar variational problems. Examples are position independent Lagrangians, Lagrangians of p-Laplacian type, and Lagrangians leading to nonlinear Poisson equations. As applications we prove certain propositions concerning the nonlinear Poisson equation and its generalisations, and the equivalence of admissible and inner variations for the systems under consideration.
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Faliagas, A.C. On the Equivalence of Euler-Lagrange and Noether Equations. Math Phys Anal Geom 19, 1 (2016). https://doi.org/10.1007/s11040-016-9203-3
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DOI: https://doi.org/10.1007/s11040-016-9203-3
Keywords
- Calculus of variations
- Noether
- Euler-lagrange
- Equivalence
- Nonlinear poisson
- Conservation laws
- Energy-momentum tensor
- Stress tensor