The Implicit Function Theorem asserts that there exists a ball of non zero 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 behaviour of solution maps is discussed.

On the Domain of the Implicit Function and Applications

PAPI M
2005-01-01

Abstract

The Implicit Function Theorem asserts that there exists a ball of non zero 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 behaviour of solution maps is discussed.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12610/556
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