Global inversion of nonsmooth mappings on Finsler manifolds

Details Global inversion of nonsmooth mappings on Finsler manifolds Global inversion of nonsmooth mappings on Finsler manifolds

2012-01-23

arxiv.org/abs/1201.4666v1

Mathematics

Functional Analysis

18 pages

Scientific paper

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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