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arXiv · 1201.4666

Global inversion of nonsmooth mappings on Finsler manifolds

Jesus A. Jaramillo·Oscar Madiedo·Luis Sanchez-Gonzalez
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Abstract

We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, using this, we obtain a version of the Hadamard integral condition for invertibility. As consequences, we deduce some global inversion and global injectivity results for Lipschitz mappings on $\mathbb{R}^n$ in terms of spectral conditions of its Clarke generalized differential.

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Jesus A. Jaramillo, Oscar Madiedo, Luis Sanchez-Gonzalez. 2012-01-23. Global inversion of nonsmooth mappings on Finsler manifolds. https://arxiv.org/abs/1201.4666

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