Artikel i vetenskaplig tidskrift, 2011
We discuss two new concepts of convergence in Lp-spaces, the socalled
weak-convergence and strong convergence, which are intermediate
between classical weak convergence and strong convergence. We also introduce
the concept of -convergence for Radon measures. Our basic tool is the classical
Gelfand representation theory. Apart from being a natural generalization of
well-known two-scale convergence theory, the present study lays the foundation
of the mathematical framework that is needed to undertake a systematic study
of deterministic homogenization problems beyond the usual periodic setting.
A few homogenization problems are worked out by way of illustration.