Symmetric Divergence-free tensors in the calculus of variations

Denis Serre

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arXiv · 2109.01448

Symmetric Divergence-free tensors in the calculus of variations

Denis Serre

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Abstract

Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called "second" variational principle, where the argument of the Lagrangian is a closed differential form. Divergence-free tensors are nothing but the second form of the Euler--Lagrange equations. The symmetry is associated with the invariance of the Lagrangian density upon the action of some orthogonal group.

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Denis Serre. 2021-09-07. Symmetric Divergence-free tensors in the calculus of variations. https://arxiv.org/abs/2109.01448

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