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## Symmetric Divergence-free tensors in the calculus of variations

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Denis Serre
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• PersonId : 1029085

#### 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.

### Dates and versions

ensl-03333651 , version 1 (03-09-2021)
ensl-03333651 , version 2 (06-09-2021)

### Identifiers

• HAL Id : ensl-03333651 , version 2
• ARXIV :

### Cite

Denis Serre. Symmetric Divergence-free tensors in the calculus of variations. 2021. ⟨ensl-03333651v2⟩

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