On two-scale convergence and related sequential compactness topics

On general two-scale convergence and its application to the characterization of G-limits

“…and see that results of the same kind as (12) hold, see [12]. In the sequel we let Ω and Y be open and bounded subsets of We define general two-scale convergence.…”

“…The following example from [12] introduces a construction of sequences {τ h } of two-scale compatible operators without involving any periodicity demands.…”

“…In Section 2 we introduce a generalization of the two-scale convergence to the case without any periodicity assumption. In Section 3 we study G-convergence for (1), where {A h } is obtained by certain two-scale techniques based on the ideas in [12]. It turns out that it is possible to find an exact criterion for when we can compute the G-limit directly.…”

A note on two scale compactness for $p = 1$

“…A few authors have touched on the problem, including Holmbom, Silfver, Svanstedt and Wellander in [16] and A. Visintin in [19], although detailed arguments seem to be unavailable in the literature. In [5,6] the authors address a related case of two-scale convergence in generalized Besicovitch spaces where there is also lack of separability.…”

On two-scale convergence and periodic unfolding

“…The two-scale limit of a sequence of x-variable functions {u ε } is a function of variables x, y; in y the local oscillations are conserved. For details see, e.g., survey papers [11], [10], [5].…”