Homogenization theory related to engineering applications, convexity and continuous inequalities

Abstract

In the first part of this paper, we give a partly new introduction to homogenization theory based on some new ideas in convexity theory (see \cite{NP}), and so-called inequalities in continuous form (see \cite{NPV}). Moreover, we present some examples of how homogenization theory can be used to derive concrete algorithms for solving important engineering problems. Some literature (including 30 books) and ideas to support these applications are mentioned. Concerning the history we have complemented the recent description in the literature by giving a more complete description of the mostly engineering inspired introduction and development of homogenization theory in the Nordic countries. Finally, we briefly describe some theoretical results and questions, which have their roots from this engineering approach and which have influenced the development of this fascinating area.