## Arkiv för Matematik

• Ark. Mat.
• Volume 55, Number 1 (2017), 217-228.

### Invertibility of nonsmooth mappings

#### Abstract

Let $F : \mathbb{R}^N \to \mathbb{R}^N$ be a locally Lipschitz continuous function. We prove that $F$ is a global homeomorphism or only injective, under suitable assumptions on the subdifferential $\partial F(x)$. We use variational methods, nonsmooth inverse function theorem and extensions of the Hadamard–Levy Theorem. We also address questions on the Markus–Yamabe conjecture.

#### Note

M. Montenegro has been supported by CNPq.

#### Note

A. Presoto has been supported by FAPESP.

#### Article information

Source
Ark. Mat., Volume 55, Number 1 (2017), 217-228.

Dates
Revised: 1 March 2017
First available in Project Euclid: 2 February 2018

https://projecteuclid.org/euclid.afm/1517535610

Digital Object Identifier
doi:10.4310/ARKIV.2017.v55.n1.a11

Mathematical Reviews number (MathSciNet)
MR3711150

Zentralblatt MATH identifier
1379.26007

#### Citation

Montenegro, Marcelo; Presoto, Adilson E. Invertibility of nonsmooth mappings. Ark. Mat. 55 (2017), no. 1, 217--228. doi:10.4310/ARKIV.2017.v55.n1.a11. https://projecteuclid.org/euclid.afm/1517535610