An Inverse Function Theorem in Frechet Spaces
Functional Analysis
2015-05-20 v1
Abstract
I present an inverse function theorem for differentiable maps between Frechet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue's dominated convergence theorem and Ekeland's variational principle. As a consequence, the assumptions are substantially weakened: the map F to be inverted is not required to be C^2, or even C^1, or even Frechet-differentiable.
Keywords
Cite
@article{arxiv.1011.1288,
title = {An Inverse Function Theorem in Frechet Spaces},
author = {Ivar Ekeland},
journal= {arXiv preprint arXiv:1011.1288},
year = {2015}
}
Comments
to appear, Annales de l'Institut Henri Poincare, Analyse Non Lineaire