Calculus of Variations and Geometric Measure Theory

N. Ansini - A. Braides

Homogenization of Oscillating Boundaries and Applications to Thin Films

created on 28 Dec 2001
modified by ansini on 17 Jan 2006


Published Paper

Inserted: 28 dec 2001
Last Updated: 17 jan 2006

Journal: J. d'Analyse Mathématique
Volume: 83
Pages: 151-182
Year: 2001


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.