Implicit Functions and Solution Mappings

a View from Variational Analysis
Buch | Hardcover
388 Seiten
2009 | 1st Edition. 2nd Printing. 2009
Springer-Verlag New York Inc.
978-0-387-87820-1 (ISBN)

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Implicit Functions and Solution Mappings - Asen L. Dontchev, R. Tyrrell Rockafellar
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This text on the implicit function paradigm is a self-contained reference that unifies a collection of many results scattered throughout other literature. It contains numerous exercises and a large amount of historical information.
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.

Functions Defined Implicitly by Equations.- Implicit Function Theorems for Variational Problems.- Regularity properties of set-valued solution mappings.- Regularity Properties Through Generalized Derivatives.- Regularity in infinite dimensions.- Applications in Numerical Variational Analysis.

Erscheint lt. Verlag 1.6.2009
Reihe/Serie Springer Monographs in Mathematics
Zusatzinfo 12 black & white illustrations, biography
Verlagsort New York, NY
Sprache englisch
Maße 156 x 234 mm
Gewicht 719 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Finanz- / Wirtschaftsmathematik
ISBN-10 0-387-87820-3 / 0387878203
ISBN-13 978-0-387-87820-1 / 9780387878201
Zustand Neuware
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