Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form
Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form
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DOI：
10.1007/s42985-020-00017-z
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Xiaoqin Guo;H. Tran;Yifeng Yu
中科院分区：
文献类型：
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作者：
Xiaoqin Guo;H. Tran;Yifeng Yu
研究了非发散形式线性椭圆型方程周期均匀化的最优收敛速度。我们得到了最佳收敛速度是或依赖于扩散矩阵A，源项f，和边界数据。此外，我们还证明了给出最优速率的扩散矩阵集A在周期、对称和正定矩阵集中是开的和稠密的，这意味着一般来说，最优速率是。
We study and characterize the optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form. We obtain that the optimal rate of convergence is eitherordepending on the diffusion matrixA, source termf, and boundary datag. Moreover, we show that the set of diffusion matricesAthat give optimal rateis open and dense in the set ofperiodic, symmetric, and positive definite matrices, which means that generically, the optimal rate is.