Existence of a Variational Principle for PDEs with Symmetries and Current Conservation
Differential Geometry
2019-10-07 v2
Abstract
We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. We reverse this statement and prove that a differential equation which satisfies sufficiently many symmetries and corresponding conservation laws leads to a variational functional whose Euler-Lagrange equation is the given differential equation.
Keywords
Cite
@article{arxiv.1906.10976,
title = {Existence of a Variational Principle for PDEs with Symmetries and Current Conservation},
author = {Markus Dafinger},
journal= {arXiv preprint arXiv:1906.10976},
year = {2019}
}