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Journal of Functional Analysis, ISSN 0022-1236, 12/2017, Volume 273, Issue 12, pp. 3875 - 3900
We prove an abstract Nash–Moser implicit function theorem which, when applied to control and Cauchy problems for PDEs in Sobolev class, is sharp in terms of the loss of regularity of the solution of the problem with respect to the data... 
Control of PDEs | Nash–Moser implicit function theorem | Quasi-linear PDEs | MATHEMATICS | Nash-Moser implicit function theorem | PERTURBATIONS | WELL-POSEDNESS | MANIFOLDS | BOUNDARY | EVOLUTION-EQUATIONS | LOCAL-CONTROLLABILITY
Journal Article
Formalized Mathematics, ISSN 1898-9934, 12/2017, Volume 25, Issue 4, pp. 269 - 281
In this article, we formalize in Mizar [1], [3] the existence and uniqueness part of the implicit function theorem... 
version: 8.1.06 5.45.1311 | identifier: NDIFF 8 | 26B10 53A07 03B35 | Banach fixed point theorem | implicit function theorem | Lipschitz continuity
Journal Article
Formalized Mathematics, ISSN 1426-2630, 07/2019, Volume 27, Issue 2, pp. 117 - 131
In this article, we formalize differentiability of implicit function theorem in the Mizar system [3], [1... 
differentiability | 47A05 | 26B10 | 47J07 | 53A07 | implicit function | 03B35 | implicit function theorem | Lipschitz continuity | lipschitz continuity | 47a05 | 26b10 | 47j07 | 53a07 | 03b35
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 11/2015, Volume 269, Issue 9, pp. 2813 - 2844
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices... 
Free noncommutative functions | Operator spaces | Implicit/inverse function theorem | Nilpotent matrices | MATHEMATICS | RATIONAL FUNCTIONS | FREE HOLOMORPHIC-FUNCTIONS | UNIT BALL
Journal Article
2013, 1. Aufl., Modern Birkhäuser classics, ISBN 146145980X, 172
The implicit function theorem is part of the bedrock of mathematical analysis and geometry... 
Implicit functions | Mathematics
eBook
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2014, Volume 414, Issue 1, pp. 259 - 272
The implicit function theorem (IFT) can be used to deduce the differentiability of an implicit mapping S:u{mapping... 
Differentiability | Implicit function theorem | Quasilinear partial differential equations | VARIATIONAL-INEQUALITIES | MATHEMATICS | MATHEMATICS, APPLIED | TORSION PROBLEM | 1ST | 2ND-ORDER | LINEAR ELLIPTIC-EQUATIONS | OPTIMALITY CONDITIONS
Journal Article
Mathematical programming, ISSN 1436-4646, 2009, Volume 123, Issue 1, pp. 139 - 159
Journal Article
Annales de l'Institut Henri Poincaré. Analyse non linéaire, ISSN 0294-1449, 2011, Volume 28, Issue 1, pp. 91 - 105
I present an inverse function theorem for differentiable maps between Fréchet spaces which contains the classical theorem of Nash and Moser as a particular case... 
Fréchet space | Implicit function theorem | Nash–Moser theorem | Inverse function theorem | Nash-Moser theorem | DIFFERENTIAL EQUATIONS | MATHEMATICS, APPLIED | Frechet space | VARIATIONAL-PROBLEMS | NASH | Mathematics - Functional Analysis
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 10/2012, Volume 22, Issue 5, pp. 1062 - 1123
We prove a global implicit function theorem. In particular we show that any Lipschitz map $${f : \mathbb{R}^{n} \times \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}}$$ (with n-dim. image... 
54E40 | 42C99 | 28A75 | Uniform rectifiability | Big pieces | Reifenberg flat | 53C23 | Analysis | Bi-Lipschitz extension | Implicit function theorem | Mathematics | Sard’s Theorem | Sard's Theorem | M-SMOOTH FUNCTION | C-M | METRIC-SPACES | SOBOLEV EXTENSION | SMALL CONSTANT | PARAMETERIZATIONS | MATHEMATICS | RECTIFIABLE SETS | MAPPINGS | DOMAINS | CHORD ARC SURFACES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 338, Issue 1, pp. 11 - 22
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 05/2009, Volume 19, Issue 1, pp. 206 - 293
..., Basel 2009 GAFA Geometric And Functional Analysis A GENERAL FREDHOLM THEORY II: IMPLICIT FUNCTION THEOREMS Helmut Hofer, Krzysztof Wysocki and Eduard Zehnder... 
M -polyfolds | sc-Banach spaces | Fredholm sections of M -polyfold bundles | Secondary 58C99 | Analysis | Primary 58B99 | Mathematics | sc-smoothness | implicit function theorem | Implicit function theorem | M-polyfolds | Fredholm sections of M-polyfold bundles | Sc-smoothness | Sc-Banach spaces | MATHEMATICS | GEOMETRY | Universities and colleges
Journal Article
Differential geometry and its applications, ISSN 0926-2245, 2019, Volume 65, pp. 176 - 211
.... First, using Glöckner's inverse function theorem, we show that the linear action of a compact Lie group... 
Nash–Moser inverse function theorem | Slice theorem | Lie group actions | Orbit type stratification | Infinite-dimensional geometry | MATHEMATICS | MATHEMATICS, APPLIED | MOTION | SPACES | Nash-Moser inverse function theorem | IMPLICIT FUNCTIONS
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 02/2016, Volume 16, Issue 1, pp. 87 - 94
In this paper, we derive generalized versions of the results on the existence, uniqueness and continuous differentiability of a global implicit function obtained in [5... 
Mountain Pass Theorem | Global Implicit Function Theorem | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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