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.
Funding Statement
M. Montenegro has been supported by CNPq.
A. Presoto has been supported by FAPESP.
Citation
Marcelo Montenegro. Adilson E. Presoto. "Invertibility of nonsmooth mappings." Ark. Mat. 55 (1) 217 - 228, September 2017. https://doi.org/10.4310/ARKIV.2017.v55.n1.a11
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