THE IMPLICIT FUNCTION THEOREM WHEN THE PARTIAL JACOBIAN MATRIX IS ONLY CONTINUOUS AT THE BASE POINT

Oswaldo de Oliveira

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THE IMPLICIT FUNCTION THEOREM WHEN THE PARTIAL JACOBIAN MATRIX IS ONLY CONTINUOUS AT THE BASE POINT

机译：局部雅可比矩阵仅在基点处连续时的隐函数定理

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This article presents an elementary proof of the Implicit Function Theorem for differentiable maps F(x, y), defined on a finite-dimensional Euclidean space, with 6F/6y(x, y) only continuous at the base point. In the case of a single scalar equation this continuity hypothesis is not required. A stronger than usual version of the Inverse Function Theorem is also shown. The proofs rely on the mean-value and the intermediate-value theorems and Darboux's property (the intermediate-value property for derivatives). These proofs avoid compactness arguments, fixed-point theorems, and integration theory.

机译：本文介绍了在有限维欧几里得空间上定义的可微映射F（x，y）的隐函数定理的基本证明，其中6F / 6y（x，y）仅在基点处连续。在单个标量方程的情况下，不需要连续性假设。还显示了比平常函数更强大的逆函数定理。证明依赖于均值和中值定理以及Darboux的属性（导数的中值属性）。这些证明避免了紧性论证，定点定理和积分理论。

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来源
《Real analysis exchange》 |2016年第2期|377-388|共12页
作者
Oswaldo de Oliveira;
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作者单位

Department of Mathematics, Universidade de Sao Paulo, Sao Paulo, SP 05508-090, Brasil;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Implicit Function Theorems; Calculus of Vector Functions; Jacobians; Functions of Several Variables;

机译：隐函数定理;向量函数演算;雅各布主义者几个变量的功能;

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专利

1. Implicit Function Theorem for Systems of Polynomial Equations with Vanishing Jacobian and Its Application to Flexible Polyhedra and Frameworks [J] . Victor Alexandrov Monatshefte für Mathematik . 2001,第4期

机译：消失雅可比多项式方程组的隐函数定理及其在柔性多面体和框架中的应用。
2. Besicovitch-Federer projection theorem for continuously differentiable mappings having constant rank of the Jacobian matrix [J] . Galeski Jacek Mathematische Zeitschrift . 2018,第3a4期

机译：BESICOVITCH-FEDERER投影定理对于具有恒定等级的连续可微分映射的雅各比矩阵
3. The plenary hull of the generalized jacobian matrix and the inverse function theorem in subdifferential calculus [J] . Telma Caputti Revista de la Unión Matemática Argentina . 1983,第3a4期

机译：亚微积分中广义雅可比矩阵的全壳和逆函数定理
4. A Feasible Model-Based OPC Algorithm Using Jacobian Matrix of Intensity Distribution Functions [C] . Ye Chen, Kechih Wu, Zheng Shi, Conference on Optical Microlithography XX pt.1 . 2007

机译：基于强度分布函数雅可比矩阵的基于模型的可行OPC算法
5. A matrix version of corona theorem for algebras of functions on reproducing kernel Hilbert spaces. [D] . Zhang, Xinjun. 2004

机译：用于重现内核希尔伯特空间的函数代数的电晕定理的矩阵形式。
6. IMPLICIT FUNCTION THEOREM FOR QUASI-ANALYTIC AND RELATED CLASSES OF FUNCTIONS [O] . T. P. G. Liverman 1956

机译：拟分析及相关函数类的隐函数定理
7. Implicit Function Theorem for Systems of Polynomial Equations with Vanishing Jacobian and Its Application to Flexible Polyhedra and Frameworks [O] . Victor Alexandrov 2001

机译：消失雅可比的多项式方程系统隐含功能定理及其在柔性多面型和框架中的应用
8. Automatic Programming System for PDEs (Partial Differential Equations) Based on a Relational Model of Continuous Physics Problems and a Functional Model of Mathematical Analysis. [R] . Balaban, D. J., Garbarini, J. P. 1988

机译：基于连续物理问题关联模型和数学分析功能模型的偏微分方程自动编程系统（偏微分方程）。

THE IMPLICIT FUNCTION THEOREM WHEN THE PARTIAL JACOBIAN MATRIX IS ONLY CONTINUOUS AT THE BASE POINT

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