具有低扩散率和高扩散率区域的局部周期介质均匀化的校正估计
Corrector estimates for the homogenization of a locally-periodic medium with areas of low and high diffusivity
摘要：
我们证明了均匀化极限$ε\to 0$的线性传输问题的对流扩散（反应）系统的低和高扩散率的地区，其中$ε$是一个合适的尺度参数的收敛速度的上界。在这种方式下，我们证明了正式的均匀化渐近由我们前面得到的收敛速度（校正估计）的上界。校正估计证明的主要内容包括具有指定平均的快速振荡函数的积分估计、宏观重构算子的性质、能量界和额外的两尺度正则性估计。整个过程基本上依赖于对极限双尺度问题的分析的良好理解。
英文摘要：
We prove an upper bound for the convergence rate of the homogenization limit $ε\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $ε$ is a suitable scale parameter. On this way, we justify the formal homogenization asymptotics obtained by us earlier by proving an upper bound for the convergence rate (a corrector estimate). The main ingredients of the proof of the corrector estimate include integral estimates for rapidly oscillating functions with prescribed average, properties of the macroscopic reconstruction operators, energy bounds and extra two-scale regularity estimates. The whole procedure essentially relies on a good understanding of the analysis of the limit two-scale problem.
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