Calculus of Variations and Geometric Measure Theory

I. Anello - A. Braides - F. Caragiulo

A note on the homogenization of incommensurate thin films

created by braidesa on 22 Dec 2022
modified on 01 Sep 2023


Published Paper

Inserted: 22 dec 2022
Last Updated: 1 sep 2023

Journal: Math. Meth. Appl. Sci.
Volume: 46
Pages: 15655-15666
Year: 2023
Doi: 10.1002/mma.9418

ArXiv: 2212.11189 PDF


Dimension-reduction homogenization results for thin films have been obtained under hypotheses of periodicity or almost-periodicity of the energies in the directions of the mid-plane of the film. In this note we consider thin films, obtained as sections of a periodic medium with a mid-plane that may be incommensurate; that is, not containing periods other than 0. A geometric almost-periodicity argument similar to the cut-and-project argument used for quasicrystals allows to prove a general homogenization result.