Generalization of unfolding operator for highly oscillating smooth boundary domains and homogenization

Unfolding operators have been introduced and used to study homogenization problems. Initially, they were introduced for problems with rapidly oscillating coefficients and porous domains. Later, this has been developed for domains with oscillating boundaries, typically with rectangular or pillar type boundaries which are classified as non-smooth. In this article, we develop new unfolding operators, where the oscillations can be smooth and hence they have wider applications. We have demonstrated by developing unfolding operators for circular domains with rapid oscillations with high amplitude of O(1) to study the homogenization of an elliptic problem.