On two-scale convergence (Q5917465)

In this paper the author surveyed some phenomena in two-scale convergence. The author discusses the original definitions by Nguetseng and Allaive. Moreover they show that alternative definition brings some advantage, for example, strong two-scale convergence is defined more naturally or it avoids some obstacles with a proof of two-scale compactness property. The author indicates that the notion of two-scale convergence can be generalized on so-called \(m\)-scale convergences that is one can consider sequences of functions \(u_n(x)= u(x,n_1x, \dots,n_{m-1}x)\) in \(L^p(\Omega)\).