Local inversion for differentiable functions and the Darboux property

DOI10.1112/S0025579300016132zbMath1051.26009OpenAlexW2122710454MaRDI QIDQ4817673

Jean Saint Raymond

Publication date: 15 September 2004

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0025579300016132

zbMATH Keywords

differentiable functionsimplicit function theoremDarboux propertylocal inversion

Mathematics Subject Classification ID

Implicit function theorems, Jacobians, transformations with several variables (26B10) Implicit function theorems; global Newton methods on manifolds (58C15) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)

Related Items (13)

On the mixing time of Kac's walk and other high-dimensional Gibbs samplers with constraints ⋮ Remarks on the infinite‐dimensional counterparts of the Darboux theorem ⋮ Inverse function theorems and Jacobians over metric spaces ⋮ New inverse and implicit function theorems for differentiable maps with isolated critical points ⋮ A metric approach to elastic reformations ⋮ Hadamard’s theorem for mappings with relaxed smoothness conditions ⋮ On the range of the derivative of Gâteaux-smooth functions on separable Banach spaces ⋮ Equidimensional isometric extensions ⋮ Open and surjective mapping theorems for differentiable maps with critical points ⋮ Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces ⋮ Application of methods of ordinary differential equations to global inverse function theorems ⋮ A note on a global invertibility of mappings onRⁿ ⋮ In the self-contact problem in nonlinear elasticity

Cites Work

• Smooth negligibility of compact sets in infinite-dimensional Banach spaces, with applications

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