Surjection and inversion for locally Lipschitz maps between Banach spaces
Functional Analysis
2022-04-20 v1
Abstract
We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition for locally Lipschitz functionals in terms of the Clarke subdifferential, as well as the notion of pseudo-Jacobians in the infinite-dimensional setting, which are the analog of the pseudo-Jacobian matrices defined by Jeyakumar and Luc. Using these notions, we derive our results about existence and uniqueness of solution for nonlinear equations. In particular, we give a version of the classical Hadamard integral condition for global invertibility in this context.
Cite
@article{arxiv.1812.00951,
title = {Surjection and inversion for locally Lipschitz maps between Banach spaces},
author = {Olivia Gutú and Jesús A. Jaramillo},
journal= {arXiv preprint arXiv:1812.00951},
year = {2022}
}