Rapidly oscillating periodic functions

Abstract In this chapter we study a relevant class of periodic oscillating functions, which plays an essential role in homogenization theory. We turn our attention, in particular, to functions of the form where a is a periodic function and where, from now on, ε > 0 takes its values in a sequence which tends to zero. Let us point out that if a is Y-periodic (see Definition 2.1 below), then a ε is εY-periodic. Moreover, as can be seen in the examples below, the smaller ε is, the more rapid are the oscillations.