A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotics for non-uniformly elliptic problems with highly oscillating coefficients are explicitly constructed. An essential feature of the new technique is that it relates homogenisation limits to a class of time-dispersive media.

中文翻译：

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临界对比度 PDE 的有效行为：微共振、频率转换和时间色散特性。一世

通过 Dirichlet-to-Neumann 算子的显式渐近分析，提出了一种用于周期性 PDE 的临界对比度均匀化的新方法。明确构造了具有高振荡系数的非均匀椭圆问题的范数解析渐近。新技术的一个基本特征是它将同质化限制与一类时间色散介质相关联。