Lipschitz Functions

✍ Scribed by Cobzaş, Ş.;Miculescu, R.;Nicolae, A.

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 604
• Series: Volume 2241 of Lecture notes in mathematics
• Category: Library

✦ Synopsis

The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results. Among the included topics we mention: characterizations of Lipschitz functions and relations with other classes of functions, extension results for Lipschitz functions and Lipschitz partitions of unity, Lipschitz free Banach spaces and their applications, compactness properties of Lipschitz operators, Bishop-Phelps type results for Lipschitz functionals, applications to best approximation in metric and in metric linear spaces, Kantorovich-Rubinstein norm and applications to duality in the optimal transport problem, Lipschitz mappings on geodesic spaces. The prerequisites are basic results in real analysis, functional analysis, measure theory (including vector measures) and topology, which, for reader's convenience, are surveyed in the first chapter of the book.

✦ Table of Contents

1 Prerequisites..............1
2 Basic Facts Concerning Lipschitz Functions..............99
3 Relations with Other Classes of Functions..............143
4 Extension Results for Lipschitz Mappings..............211
5 Extension Results for Lipschitz Mappings in Geodesic Spaces..............252
6 Approximations Involving Lipschitz Functions..............317