Implicit functions and solution mappings a view from variational analysis /
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of sol...
| Main Author: | Dontchev, A. L., 1948- |
|---|---|
| Other Authors: | Rockafellar, R. Tyrrell, 1935-, SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht ; New York :
Springer,
©2009.
Dordrecht ; New York : [2009] |
| Physical Description: |
1 online resource (xii, 375 pages) : illustrations. |
| Series: |
Springer monographs in mathematics.
|
| Subjects: |
| Summary: |
The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. The first chapter of the book treats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomes gradually more advanced, and considers implicit mappings defined by relations other than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided. This valuable book is a major achievement and is sure to become a standard reference on the topic. |
|---|---|
| Item Description: |
Includes bibliographical references and index. Preface -- Acknowledgements -- Functions Defined Implicitly by Equations -- Implicit Function Theorems for Variational Problems -- Regularity Properties of Set-Value Solution Mappings -- Regularity Properties Through Generalized Derivatives -- Regularity in Infinite Dimensions -- Applications in Numerical Variational Analysis -- References -- Notation -- Index.- The implicit function theorem is one of the most important theorems in analysis and its many variants are basic tools in partial differential equations and numerical analysis. This book treats the implicit function paradigm in the classical framework and beyond, focusing largely on properties of solution mappings of variational problems. The purpose of this self-contained work is to provide a reference on the topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. The first chapter of the book treats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomes gradually more advanced, and considers implicit mappings defined by relations other than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided. This valuable book is a major achievement and is sure to become a standard reference on the topic. University staff and students only. Requires University Computer Account login off-campus. |
| Physical Description: |
1 online resource (xii, 375 pages) : illustrations. |
| Bibliography: |
Includes bibliographical references and index. |
| ISBN: |
9780387878218 0387878211 9780387878201 0387878203 |
| ISSN: |
1439-7382. |
| Access: |
University staff and students only. Requires University Computer Account login off-campus. |