Symmetric Divergence-free tensors in the calculus of variations

2021/09/03 by Denis Serre, Serre, Denis
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2109.01448

openalex publication_date 2021/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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