Some mathematical and engineering aspects of the homogenization theory

Sammanfattning: This thesis is devoted to some problems connected to the theory of homogenization of partial differential operators. The thesis consists of an elementary introduction and five different parts, A-E. In the introduction we give an elementary presentation of the basic ideas in the homogenization theory. Moreover, the introduction also serves as an overview of the field and points out where the results contained in this thesis fit in. The first part, Part A, consists of two papers with a complementary appendix and deals some purely theoretical parts of homogenization theory. Part B consists of one paper dealing with bounds of the homogenized operator. The third part, Part C, consists of two papers concerning some computational aspects of homogenization. Part D consists of two papers which show how the theoretical results from the homogenization theory can be practically used in composites engineering. Finally, Part E consists of two papers presented at international conferences, which consider some further mathematical and engineering aspects of the homogenization method.