Arkiv för Matematik

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

Invertibility of nonsmooth mappings

Marcelo Montenegro and Adilson E. Presoto

Full-text: Open access

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
Received: 24 February 2016
Revised: 1 March 2017
First available in Project Euclid: 2 February 2018

Permanent link to this document
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

Subjects
Primary: 26A16: Lipschitz (Hölder) classes 26B10: Implicit function theorems, Jacobians, transformations with several variables 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 49J40: Variational methods including variational inequalities [See also 47J20] 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56]

Keywords
injectivity invertibility homeomorphism Lipschitz continuous functions Markus–Yamabe Conjecture

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


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