On the domain of the implicit function and applications. Issue 3 (11th July 2005)

• Record Type: Journal Article
• Authors: Papi, Marco
• Is Part Of: Journal of inequalities and applications. Volume 2005:Issue 3(2005)
• Page Start: 221
• Page End: 234
• Publication Date: 2005-07-11
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/JIA.2005.221
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : 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.