A Non-Newtonian Noether's Symmetry Theorem
Classical Analysis and ODEs
2023-06-06 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
The universal principle obtained by Emmy Noether in 1918, asserts that the invariance of a variational problem with respect to a one-parameter family of symmetry transformations implies the existence of a conserved quantity along the Euler-Lagrange extremals. Here we prove Noether's theorem for the recent non-Newtonian calculus of variations. The proof is based on a new necessary optimality condition of DuBois-Reymond type.
Keywords
Cite
@article{arxiv.2111.11559,
title = {A Non-Newtonian Noether's Symmetry Theorem},
author = {Delfim F. M. Torres},
journal= {arXiv preprint arXiv:2111.11559},
year = {2023}
}
Comments
This is a preprint of a paper whose final and definite form is published in 'Applicable Analysis', Print ISSN: 0003-6811, Online ISSN: 1563-504X. Submitted 02-Aug-2021, Accepted for publication 22-Nov-2021