Homogenization effects on non-local functionals

Abstract

We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the Γ-limit for constant target functions, revealing how the interplay between periodicity and non-locality forces the minimizing sequences to develop highly oscillating microstructures. As a natural consequence, we establish that the effective macroscopic functional fails to admit a standard double-integral representation.

References in corpus (4)

• Ising models with long-range dipolar and short-range ferromagnetic interactions
• Exact periodic stripes for a minimizers of a local/non-local interaction functional in general dimension
• Homogenization of random convolution energies in heterogeneous and perforated domains
• Beyond the classical Cauchy-Born rule