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

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

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

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

Free noncommutative functions | Operator spaces | Implicit/inverse function theorem | Nilpotent matrices | MATHEMATICS | RATIONAL FUNCTIONS | FREE HOLOMORPHIC-FUNCTIONS | UNIT BALL

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2016, Volume 156, Issue 1, pp. 257 - 270

... of Robinson’s implicit function theorem for nonsmooth generalized equations in finite dimensions, which reduces...

Robinson’s inverse function theorem | Theoretical, Mathematical and Computational Physics | Mathematics | Clarke’s inverse function theorem | 90C31 | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | 49K40 | Numerical Analysis | Generalized equation | Strict pre-derivative | Strong metric regularity | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | IMPLICIT-FUNCTION THEOREM | Robinson's inverse function theorem | Clarke's inverse function theorem | Studies | Computer programming | Theorems | Banach spaces | Functions (mathematics) | Mathematical analysis | Paper | Inverse | Banach space | Mathematical programming

Robinson’s inverse function theorem | Theoretical, Mathematical and Computational Physics | Mathematics | Clarke’s inverse function theorem | 90C31 | Mathematical Methods in Physics | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | 49K40 | Numerical Analysis | Generalized equation | Strict pre-derivative | Strong metric regularity | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | IMPLICIT-FUNCTION THEOREM | Robinson's inverse function theorem | Clarke's inverse function theorem | Studies | Computer programming | Theorems | Banach spaces | Functions (mathematics) | Mathematical analysis | Paper | Inverse | Banach space | Mathematical programming

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

Implicit functions | Mathematics

eBook

2002, ISBN 9783764342852, xi, 163

Book

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

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

Optimization letters, ISSN 1862-4480, 2018, Volume 13, Issue 8, pp. 1745 - 1755

The paper is devoted to the implicit function theorem involving singular mappings...

Singularity | Computational Intelligence | p -Regularity | Operations Research/Decision Theory | Generalized equation | Implicit function theorem | Mathematics | Numerical and Computational Physics, Simulation | Multifunction | Optimization | Tangent cone | p-Regularity | Mathematics - Functional Analysis

Singularity | Computational Intelligence | p -Regularity | Operations Research/Decision Theory | Generalized equation | Implicit function theorem | Mathematics | Numerical and Computational Physics, Simulation | Multifunction | Optimization | Tangent cone | p-Regularity | Mathematics - Functional Analysis

Journal Article

Mathematical programming, ISSN 1436-4646, 2009, Volume 123, Issue 1, pp. 139 - 159

In an extension of Newton’s method to generalized equations, we carry further the implicit function theorem paradigm and place it in the framework of a mapping acting from the parameter and the starting point to the set...

Generalized equations | Variational analysis | Theoretical, Mathematical and Computational Physics | Newton’s method | Mathematics | Mathematical Methods in Physics | 49J53 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 49K40 | Numerical Analysis | Inverse function theorems | Combinatorics | Perturbations | Implicit function theorems | 65J15 | Strong regularity | Variational inequalities | 90C3l | Newton's method | MATHEMATICS, APPLIED | STABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MESH-INDEPENDENCE | Studies | Theorems | Mathematical programming

Generalized equations | Variational analysis | Theoretical, Mathematical and Computational Physics | Newton’s method | Mathematics | Mathematical Methods in Physics | 49J53 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | 49K40 | Numerical Analysis | Inverse function theorems | Combinatorics | Perturbations | Implicit function theorems | 65J15 | Strong regularity | Variational inequalities | 90C3l | Newton's method | MATHEMATICS, APPLIED | STABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MESH-INDEPENDENCE | Studies | Theorems | Mathematical programming

Journal Article

Revista Matematica Iberoamericana, ISSN 0213-2230, 2018, Volume 34, Issue 3, pp. 1387 - 1400

...+m, by an argument based on the implicit function theorem.

Applications of the implicit function theorem | Multilinear algebra methods in real analysis | Tangency set of a submanifold with respect to a distribution | multilinear algebra methods in real analysis | MATHEMATICS | applications of the implicit function theorem | SIZE

Applications of the implicit function theorem | Multilinear algebra methods in real analysis | Tangency set of a submanifold with respect to a distribution | multilinear algebra methods in real analysis | MATHEMATICS | applications of the implicit function theorem | SIZE

Journal Article

Econometrica, ISSN 0012-9682, 2012, Volume 80, Issue 1, pp. 425 - 454

The delta method and continuous mapping theorem are among the most extensively used tools in asymptotic derivations in econometrics...

Maximum likelihood estimation | Estimation bias | Mathematical theorems | NOTES AND COMMENTS | Economic theory | Estimation theory | Inference | Unbiased estimators | Econometrics | Estimators | Estimation methods | exact bias | Binding function | delta method | implicit continuous maps | indirect inference | maximum likelihood | Indirect inference | Maximum likelihood | Implicit continuous maps | Delta method | Exact bias | MEDIAN-UNBIASED ESTIMATION | PRICES | BIAS | STATISTICS & PROBABILITY | SERIAL-CORRELATION COEFFICIENT | LIMIT THEORY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | UNIT-ROOT | TIME-SERIES | SYSTEMS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | VARIANCE

Maximum likelihood estimation | Estimation bias | Mathematical theorems | NOTES AND COMMENTS | Economic theory | Estimation theory | Inference | Unbiased estimators | Econometrics | Estimators | Estimation methods | exact bias | Binding function | delta method | implicit continuous maps | indirect inference | maximum likelihood | Indirect inference | Maximum likelihood | Implicit continuous maps | Delta method | Exact bias | MEDIAN-UNBIASED ESTIMATION | PRICES | BIAS | STATISTICS & PROBABILITY | SERIAL-CORRELATION COEFFICIENT | LIMIT THEORY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MODELS | UNIT-ROOT | TIME-SERIES | SYSTEMS | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS | VARIANCE

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2009, Volume 117, Issue 1, pp. 129 - 147

.... In fact, his result covered much of the classical implicit function theorem, if not quite all, but went far beyond that in ideas and format. Here...

Mathematical and Computational Physics | Mathematics | Inverse and implicit function theorems | 90C31 | Mathematical Methods in Physics | 49J53 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Semiderivatives | 47J07 | Lipschitz modulus | Combinatorics | Calmness | First-order approximations | Variational inequalities | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | first-order approximations | GENERALIZED EQUATIONS | inverse and implicit function theorems | calmness | MAPPINGS | OPTIMIZATION | semiderivatives | variational inequalities | Studies | Optimization | Mathematical programming

Mathematical and Computational Physics | Mathematics | Inverse and implicit function theorems | 90C31 | Mathematical Methods in Physics | 49J53 | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Semiderivatives | 47J07 | Lipschitz modulus | Combinatorics | Calmness | First-order approximations | Variational inequalities | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | first-order approximations | GENERALIZED EQUATIONS | inverse and implicit function theorems | calmness | MAPPINGS | OPTIMIZATION | semiderivatives | variational inequalities | Studies | Optimization | Mathematical programming

Journal Article

Mathematical programming, ISSN 1436-4646, 2013, Volume 139, Issue 1-2, pp. 301 - 326

In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings...

Generalized equations | Theoretical, Mathematical and Computational Physics | Error bound | Mathematics | Mathematical Methods in Physics | Perturbation stability | 90C30 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Implicit multifunction | Metric regularity | Combinatorics | LOWER SEMICONTINUOUS FUNCTIONS | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | APPROXIMATIONS | STABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | MAPPINGS | ERROR-BOUNDS | OPENNESS | Computer science | Studies | Analysis | Mathematical programming | Functions (mathematics) | Theorems | Stability | Perturbation methods | Metric space | Mathematical analysis | Derivatives | Regularity

Generalized equations | Theoretical, Mathematical and Computational Physics | Error bound | Mathematics | Mathematical Methods in Physics | Perturbation stability | 90C30 | 49J53 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 49J52 | Numerical Analysis | Implicit multifunction | Metric regularity | Combinatorics | LOWER SEMICONTINUOUS FUNCTIONS | MATHEMATICS, APPLIED | SUFFICIENT CONDITIONS | APPROXIMATIONS | STABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | MAPPINGS | ERROR-BOUNDS | OPENNESS | Computer science | Studies | Analysis | Mathematical programming | Functions (mathematics) | Theorems | Stability | Perturbation methods | Metric space | Mathematical analysis | Derivatives | Regularity

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

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

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

In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained...

Metric projection | Lower semicontinuity | Normal coderivative | Implicit function theorem | Pseudo-Lipschitz property | Metric regularity | Multifunction | MATHEMATICS, APPLIED | LIPSCHITZIAN PROPERTIES | CALCULUS | lower semicontinuity | SET-VALUED MAPS | INCLUSION CONSTRAINTS | STABILITY THEORY | multifunction | implicit function theorem | pseudo-lipschitz property | MATHEMATICS | metric projection | GENERALIZED EQUATIONS | metric regularity | BANACH-SPACES | INEQUALITY SYSTEMS | normal coderivative | OPTIMIZATION

Metric projection | Lower semicontinuity | Normal coderivative | Implicit function theorem | Pseudo-Lipschitz property | Metric regularity | Multifunction | MATHEMATICS, APPLIED | LIPSCHITZIAN PROPERTIES | CALCULUS | lower semicontinuity | SET-VALUED MAPS | INCLUSION CONSTRAINTS | STABILITY THEORY | multifunction | implicit function theorem | pseudo-lipschitz property | MATHEMATICS | metric projection | GENERALIZED EQUATIONS | metric regularity | BANACH-SPACES | INEQUALITY SYSTEMS | normal coderivative | OPTIMIZATION

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

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

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

Mountain Pass Theorem | Global Implicit Function Theorem | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

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