Implicit functions and solution mappings
Subtitle: a view from variational analysis
By: Asen L. Dontchev, R. Tyrrell Rockafellar
Contributors: Rockafellar, R. Tyrrell, 1935-; SpringerLink (Online service)
Series: Springer monographs in mathematics
Publisher: Springer
Published: 2009
Place of publication: Dordrecht; New York
Language: eng
Format: [electronic resource] :
Number of pages: 375
ISBN-13: 9780387878201; 9780387878218
Subjects: Implicit functions; Mappings (Mathematics)
Description: 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.
Notes: Includes bibliographical references and index.

Mode of access: World Wide Web.