Journal of Convex Analysis 20 (2013), No. 4, 1127--1146
Copyright Heldermann Verlag 2013
Global Inversion of Nonsmooth Mappings on Finsler Manifolds
Jesús A. Jaramillo
Dep. de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
jaramil@mat.ucm.es
Óscar Madiedo
Dep. de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
oscar.reynaldo@mat.ucm.es
Luis Sánchez-González
Dep. de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
lfsanche@mat.ucm.es
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 Rn in terms of spectral conditions of its Clarke generalized differential.
Keywords: Global inversion, generalized differential, Finsler manifolds.
MSC: 49J52, 58C15
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