论文标题
椭圆形方程均质化中扩散矩阵的表征非散发形式
Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form
论文作者
论文摘要
我们表征了$ l^{\ infty} $收敛速率的扩散矩阵（\ varepsilon^2）$在非胶合形式中线性椭圆方程的定期均质化理论中。这种类型 - $ \ VAREPSILON^2 $扩散矩阵特别令人感兴趣，因为在通用情况下的最佳收敛速率仅为$ \ MATHCAL {O}（\ VAREPSILON）$。首先，我们提供了一种新类型-U \ Varepsilon^2 $扩散矩阵，确认[15]中提出的猜想。然后，我们在二维中对对角线扩散矩阵和更高维度的系统研究进行了完整的表征。
We characterize diffusion matrices that yield a $L^{\infty}$ convergence rate of $\mathcal{O}(\varepsilon^2)$ in the theory of periodic homogenization of linear elliptic equations in nondivergence-form. Such type-$\varepsilon^2$ diffusion matrices are of particular interest as the optimal rate of convergence in the generic case is only $\mathcal{O}(\varepsilon)$. First, we provide a new class of type-$\varepsilon^2$ diffusion matrices, confirming a conjecture posed in [15]. Then, we give a complete characterization of diagonal diffusion matrices in two dimensions and a systematic study in higher dimensions.
