Convex functional analysis
This is the first of two volumes which are devoted to convex functional analysis and its application to contact problems in mechanics, shape optimization problems, identification problems in mechanics and control of incompressible flow. It is devoted to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are used in various applications to mechanics and control theory. The book provides not only the bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis, but also a concise summary of definitions and theorems so that the text is self-contained. The contents includes an overview of classical abstract spaces (chapter 1), linear functionals and linear operators (chapter 2), common function spaces (Sobolev and Banach) (chapter 3), differential calculus in normed vector spaces (chapter 4), minimization functionals (chapter 5) and convex functionals (chapter 6), lower semicontinuous functionals (chapter 7). This book will be useful for those with a background in graduate mathematics who are interested in a concise summary of the main definitions and theorems in convex functional analysis.
scientific article; zbMATH DE number 2174320