Homogenization of quadratic convolution energies in periodically perforated domains
Homogenization of quadratic convolution energies in periodically perforated domains
复制标题
周期性穿孔域中二次卷积能量的均匀化
DOI：
10.1515/acv-2019-0083
复制
发表时间：
2019
影响因子：
1.7
通讯作者：
Andrey L. Piatnitski
中科院分区：
文献类型：
--
作者：
Andrea Braides;Andrey L. Piatnitski
摘要证明了穿孔区域上二次卷积能量的均匀化定理。相应的极限是狄利克雷型二次能量，其被积量由非局部单元问题公式定义。该证明依赖于一个扩展定理，该扩展定理来自于一个包含紧周期穿孔的广义类的穿孔区域。
Abstract 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.