implicit function theorem


Let Ω be an open subset of Rn×Rm and let fC1(Ω,Rm). Let (x0,y0)ΩRn×Rm. If the matrix Dyf(x0,y0) defined by


is invertiblePlanetmathPlanetmath, then there exists a neighborhoodMathworldPlanetmath URn of x0 and a functionMathworldPlanetmath gC1(U,Rm) such that

f(x,g(x))=f(x0,y0)  xU.


Title implicit function theoremMathworldPlanetmath
Canonical name ImplicitFunctionTheorem
Date of creation 2013-03-22 12:58:33
Last modified on 2013-03-22 12:58:33
Owner azdbacks4234 (14155)
Last modified by azdbacks4234 (14155)
Numerical id 12
Author azdbacks4234 (14155)
Entry type Theorem
Classification msc 26B10
Related topic FlowBoxTheorem
Related topic DerivativeAsParameterForSolvingDifferentialEquations