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.