Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

2013/11/12 by Jaramillo, Jesús A., Madiedo, Oscar, Sánchez-González, Luis
#49J52 #49J53 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1311.2815

Abstract

We study the global inversion of a continuous nonsmooth mapping f: ℝⁿ → ℝⁿ, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f, introduced by Jeyakumar and Luc, and we consider a related index of regularity for f. We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard integral condition has a natural counterpart in this setting, providing a sufficient condition for global invertibility.

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