Basics of Functional Analysis and Function Spaces

Abstract

The focus of Part II of this monograph will be, firstly, on the construction of variational formulations of the initial–boundary value problem of elastoplasticity, and, secondly, on the well-posedness of these variational problems. There are a number of tools from functional analysis that are called upon in the course of such analyses, and naturally the variational problems themselves are posed on particular function spaces. For these reasons we begin Part II by reviewing, in this chapter, those results from functional analysis that are pertinent to subsequent developments. We also collect in one place a number of results pertaining to function spaces, especially Sobolev spaces.