Some new developments and applications 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 introduction and three different parts, A-C. 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 one paper with a complementary appendix and deals with the limit behavior of the solutions of a sequence of quasi-linear equations. Part B consists of one paper with a complementary appendix in which the homogenization theory is used for the evaluation of different semi-analytical models used in the determination of the elastic properties of woven composites. The third part, Part C, consists of three papers which consider some further mathematical and engineering aspects of the homogenization method. Several numerical and experimental results are also presented and compared with theoretical results.