Asymptotic analysis of second-order boundary layer correctors
Asymptotic analysis of second-order boundary layer correctors
复制标题
二阶边界层校正器的渐近分析
DOI：
10.1080/00036811.2011.616498
复制
发表时间：
2012
影响因子：
1.1
通讯作者：
B. Vernescu
中科院分区：
文献类型：
--
作者：
D. Onofrei;B. Vernescu
在这篇文章中，我们扩展了Onofrei和Vernescu [渐近分析]中提出的思想。54（2007），pp. 103-123]，并引入适当的二阶边界层修正项，研究了经典均匀化问题的H1模误差估计，即以往的二阶边界层结果要么假设系数足够光滑（等价于假设修正项χ j，χ ij ∈ W1，∞），要么假设均匀化解u 0足够光滑，以得到阶的估计.为此，我们使用了与Cioranescu等人[C. R. Acad. Sci.巴黎，系列I 335（2002），第110页。99-104]。我们证明，在二维，非光滑系数和一般的数据，一个获得的估计的顺序。在三维空间中，假设χ j，χ ij ∈ W 1，p，p > 3，得到相同的估计.
In this article we extend the ideas presented in Onofrei and Vernescu [Asymptotic Anal. 54 (2007), pp. 103–123] and introduce suitable second-order boundary layer correctors, to study the H 1-norm error estimate for the classical problem of homogenization, i.e. Previous second-order boundary layer results assume either smooth enough coefficients (which is equivalent to assuming smooth enough correctors χ j , χ ij ∈ W 1,∞), or smooth homogenized solution u 0, to obtain an estimate of order . For this we use some ideas related to the periodic unfolding method proposed by Cioranescu et al. [C. R. Acad. Sci. Paris, Ser. I 335 (2002), pp. 99–104]. We prove that in two dimensions, for non-smooth coefficients and general data, one obtains an estimate of order . In three dimensions the same estimate is obtained assuming χ j , χ ij ∈ W 1,p , with p > 3.