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Journal of Function Spaces and Applications
Volume 3, Issue 2, Pages 125-161
http://dx.doi.org/10.1155/2005/217152

Two-scale convergence with respect to measures and homogenization of monotone operators

1Narvik University College, N-8505 Narvik, Norway
2Department of Mathematics, Luleå University of Technology, S-971 87 Luleå, Sweden

Received 1 May 2004

Academic Editor: Lars-Erik Persson

Copyright © 2005 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.

Abstract

In 1989 Nguetseng introduced two-scale convergence, which now is a frequently used tool in homogenization of partial differential operators. In this paper we discuss the notion of two-scale convergence with respect to measures. We make an exposition of the basic facts of this theory and develope it in various ways. In particular, we consider both variable Lp spaces and variable Sobolev spaces. Moreover, we apply the results to a homogenization problem connected to a class of monotone operators.