Homogenization of oscillating boundaries and applications to thin films

2000/10/02 by Nadia Ansini, Ansini, Nadia, Andrea Braides +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.math/0010011

31 pages, 7 figures

arxiv created 2000/10/02 · arxiv updated 2009/11/30

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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