Homogenization of oscillating boundaries and applications to thin films

The study carried on in this paper draws its motivation from the problem of the asymptotic description of nonlinearly elastic thin films with a fast-oscillating profile. The behaviour of such films is governed by an elastic energy, where two parameters intervene: a first parameter ε represents the thickness of the thin film and a second one δ the scale of the oscillations. The analytic description of the elastic energy is given by a functional of the form