基于$Γ$ -收敛的随机分数阶障碍问题的均匀化
Homogenization of random fractional obstacle problems via $Γ$-convergence
摘要：
利用$Γ$ -收敛方法证明了周期穿孔区域上分数阶障碍问题的均匀化结果。障碍物具有随机的大小和形状，其容量根据平稳的遍历过程进行缩放。我们使用的痕迹表示的分数Sobolev规范的加权Sobolev能量建立的Caffarelli和Silvestre，一个加权的遍历定理和加入引理在不同的域以下的方法由Ansini和Braides。我们的证明是替代那些载于文件中的Caffarelli和Mellet。
英文摘要：
$Γ$-convergence methods are used to prove homogenization results for fractional obstacle problems in periodically perforated domains. The obstacles have random sizes and shapes and their capacity scales according to a stationary ergodic process. We use a trace-like representation of fractional Sobolev norms in terms of weighted Sobolev energies established by Caffarelli and Silvestre, a weighted ergodic theorem and a joining lemma in varying domains following the approach by Ansini and Braides. Our proof is alternative to those contained in the papers by Caffarelli and Mellet.
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