TABLE OF CONTENTS The focus of Part II of this monograph will be, firstly, on the construction of variational formulations of the initial-boundary value problem of elasto-plasticity, 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.
The overviews are not intended to be comprehensive, and full details may be found in monographs devoted to functional analysis and function spaces. The text [106] by Reddy may be consulted for an introduction to functional analysis that is aimed at those interested in variational problems and finite elements. Extended summary accounts of the relevant subject matter may also be found in Zeidler [128], [131], [132] and in Dautray and Lions [30]. There exist a number of accessible accounts of function spaces and, in particular, the theory of Sobolev spaces, some examples of which are Adams [1], Dautray and Lions [30], Reddy [106], Renardy...
