Implicit functions and solution mappings: a view from variational analysis

The book is about 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 onthe topic and to provide a unified collection of a number of results which are currently scattered throughout the literature. The first chapter of the booktreats the classical implicit function theorem in a way that will be useful for students and teachers of undergraduate calculus. The remaining part becomesgradually more advanced, and considers implicit mappings defined by relationsother than equations, e.g., variational problems. Applications to numerical analysis and optimization are also provided. 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 valuable book is a major achievement and is sure to become a standard reference on the topic. An attractive blend of modern topics and classical results Authors haveincluded a nice selection of exercises for classroom use Ideal reference workwhich contains a large amount of historical material and references INDICE: Introduction.- Functions and their Inverses.- Implicit Function Theorems for Variational Problems.- Regularity Properties of Set-Valued SolutionMappings.- Regularity Properties Through Generalized Derivatives.- Regularityin Infinite Dimensions.- Numerical Variational Analysis.

• ISBN: 978-0-387-87820-1
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 375
• Fecha Publicación: 01/01/2009
• Nº Volúmenes: 1
• Idioma: Inglés