The implicit function theorem for Lipschitz functions and applications

Abstract

The subject matter of this thesis is the classical Implicit Function Theorem and its generalizations. Dictated by practical applications, it is of interest to relax the hypothesis of the standard Implicit Function Theorem as to allow for more general classes of functions. We do so by analyzing this situation in the context of the class of Lipschitz Functions. We provide several proofs, as well as applications.