Symmetric Divergence-free tensors in the calculus of variations
Analysis of PDEs
2021-09-08 v2 Mathematical Physics
math.MP
Classical Physics
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.
Keywords
Cite
@article{arxiv.2109.01448,
title = {Symmetric Divergence-free tensors in the calculus of variations},
author = {Denis Serre},
journal= {arXiv preprint arXiv:2109.01448},
year = {2021}
}