Implicit Functions and Solution Mappings

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 second edition of Implicit Functions and Solution Mappings presents an updated and more complete picture of the field by including solutions of problems that have been solved since the first edition was published, and places old and new results in a broader perspective. 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. Updates to this edition include new sections in almost all chapters, new exercises and examples, updated commentaries to chapters and an enlarged index and references section.

Covers major developments of the last five years Complements and extends significantly the material covered in the first edition Includes new solutions of problems that were open when the first edition was published

Autorentext

Asen L. Dontchev is a Professor at the Department of Mathematics at the University of Michigan. R. Tyrrell Rockafellar is a Professor at the Department of Mathematics at the University of Washington and at the Department of Industrial and Systems Engineering at the University of Florida.

Inhalt
Introduction and equation-solving background.- Solution mappings for variational problems.- Set-valued analysis of solution mappings.- Regularity properties through generalized derivatives.- Metric regularity in infinite dimensions.- Applications in numerical variational analysis.