Homogenization of Random Fractional Obstacle Problems via Γ-Convergence
Homogenization of Random Fractional Obstacle Problems via Γ-Convergence
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通过 Γ 收敛对随机分数障碍问题进行均质化
DOI：
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发表时间：
2009
期刊：
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通讯作者：
M. Focardi
中科院分区：
文献类型：
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作者：
M. Focardi
γ-收敛方法用于证明周期性穿孔域中分数障碍问题的均质化结果。障碍物具有随机的大小和形状，并且它们的容量根据平稳遍历过程而变化。我们使用[9]中建立的加权Sobolev能量来表示分数Sobolev范数，加权遍历定理和不同领域中的连接引理，遵循[2]的方法。我们的证明可以替代[7, 8]中包含的证明。
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 in [9], a weighted ergodic theorem and a joining lemma in varying domains following the approach by [2]. Our proof is alternative to those contained in [7, 8].