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Homogenization of oscillating boundaries and applications to thin films

Nadia Ansini·Andrea Braides
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Abstract

We prove a homogenization result for integral functionals in domains with oscillating boundaries, showing that the limit is defined on a degenerate Sobolev space. We apply this result to the description of the asymptotic behaviour of thin films with fast-oscillating profile, proving that they can be described by first applying the homogenization result above and subsequently a dimension-reduction technique.

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Nadia Ansini, Andrea Braides. 2000-10-02. Homogenization of oscillating boundaries and applications to thin films. https://arxiv.org/abs/math/0010011

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