Inserted: 25 mar 2009
Last Updated: 20 may 2009
Journal: C. R. Acad. Sci. Paris
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