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Journal of Function Spaces and Applications
Volume 6 (2008), Issue 2, Pages 155-176

Mathematical analysis and homogenization of the torsion problem

1Narvik University College, N-8505 Narvik, Norway
2Norut Narvik, P.O. Box 250, N-8504 Narvik, Norway
3Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Received 1 June 2007

Academic Editor: Alois Kufner

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we address the limitations of the classical formulation of the torsion problem and give a self-contained survey of the function spaces and formulations that are more suitable for analysing the torsional behavior of composite materials. We also prove some homogenization results for the torsion problem in both the periodic and stochastic setting. Our theoretical results are illustrated by numerical examples.