Open Access

On the domain of the implicit function and applications

Journal of Inequalities and Applications20052005:373250

Received: 31 July 2003

Published: 11 July 2005


The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. We derive a lower bound for the radius of this ball in the case of Lipschitz maps. Under a sign-preserving condition, we prove that an implicit function exists in the case of a set of inequalities. Also in this case, we state an estimate for the size of the domain. An application to the local Lipschitz behavior of solution maps is discussed.

Authors’ Affiliations

Istituto per le Applicazioni del Calcolo "Mauro Picone"
Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"


© Papi 2005