Global inversion of nonsmooth mappings using pseudo-Jacobian matrices

We study the global inversion of a continuous nonsmooth mapping f:Rn→Rnf:Rn→Rn, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to ff, introduced by Jeyakumar and Luc, and we consider a related index of regularity for ff. 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.