Calculus of Variations and Geometric Measure Theory

A. Braides - G. Riey - M. Solci

Homogenization of Penrose tilings

created by braidesa on 25 Mar 2009
modified on 20 May 2009


Published Paper

Inserted: 25 mar 2009
Last Updated: 20 may 2009

Journal: C. R. Acad. Sci. Paris
Volume: 347
Pages: 697-700
Year: 2009


A homogenization theorem is proved for energies which follow the geometry of an a-periodic Penrose tiling. The result is obtained by proving that the corresponding energy densities are $W^1$-almost periodic and hence also Besicovitch almost periodic, so that existing general homogenization theorems can be applied. The method applies to general quasicristalline geometries.

Keywords: Homogenization, integral functionals, Penrose tilings, almost-periodic functions