We prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The corresponding limit is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof relies on an extension theorem from perforated domains belonging to a wide class containing compact periodic perforations.

中文翻译：

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周期性穿孔域中二次卷积能量的均匀化

我们证明了在穿孔域中定义的二次卷积能量的同质化定理。相应的极限是狄利克雷型二次能量，其被积函数由非局部单元问题公式定义。该证明依赖于穿孔域的扩展定理，该域属于包含紧凑周期性穿孔的宽类。