We establish the higher order convergence rates in periodic homogenization of fully nonlinear uniformly parabolic Cauchy problems, accompanied with rapidly oscillating initial data. The higher order convergence rates are achieved by constructing the higher order initial layer correctors and the higher order interior correctors that describe the oscillatory behavior of the solutions to the given $\epsilon$-problems. In order to construct these correctors, we establish a regularity theory in the slow variables, that is, the non-oscillatory physical variables, of solutions to either the spatially periodic Cauchy problems or the cell problems, based on the classical theory for viscosity solutions.

中文翻译：

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同质化理论中的高阶收敛率 II：振荡初始数据

我们在完全非线性一致抛物线柯西问题的周期性均匀化中建立了高阶收敛率，伴随着快速振荡的初始数据。高阶收敛速度是通过构建高阶初始层校正器和高阶内部校正器来实现的，这些校正器描述给定 $\epsilon$-问题的解决方案的振荡行为。为了构造这些校正器，我们基于粘度解的经典理论，在慢变量（即非振荡物理变量）的空间周期性柯西问题或单元问题的解中建立了规律性理论。