Regularization and singular perturbation techniques for non-smooth systems

This paper is concerned with some aspects of the qualitative–geometric theory of non-smooth systems. We present a survey of the state of the art on the connection between the regularization process of non-smooth vector fields and the singular perturbation problems. As a matter of fact, the main results in our setting fill a gap between these areas. Exploiting such results, applications to constrained differential equations are discussed.