An introduction to the qualitative and quantitative theory of homogenization
An introduction to the qualitative and quantitative theory of homogenization
复制标题
均质化的定性和定量理论简介
DOI：
10.4036/iis.2018.a.01
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
S. Neukamm
中科院分区：
文献类型：
--
作者：
S. Neukamm
介绍了椭圆型偏微分方程的周期均匀化和随机均匀化。第一部分是关于周期系数和随机系数方程的定性理论，给出了基于Tartar振荡试验函数方法的统一方法。特别地，我们给出了构造随机均匀化次线性校正器的一个完备的初等论证。（这个论点也适用于椭圆系统，特别是线性弹性）。在第二部分中，我们简要讨论了用双尺度展开表示均匀化误差的方法。最后，我们讨论了离散条件下定量随机均匀化的一些结果。特别地，我们讨论了通过浓度不等式对遍历性的量化，并说明了后者与椭圆正则性理论相结合，可以量化次线性校正量和均匀化误差的增长。
We present an introduction to periodic and stochastic homogenization of ellip- tic partial differential equations. The first part is concerned with the qualitative theory, which we present for equations with periodic and random coefficients in a unified approach based on Tartar's method of oscillating test functions. In partic- ular, we present a self-contained and elementary argument for the construction of the sublinear corrector of stochastic homogenization. (The argument also applies to elliptic systems and in particular to linear elasticity). In the second part we briefly discuss the representation of the homogenization error by means of a two- scale expansion. In the last part we discuss some results of quantitative stochastic homogenization in a discrete setting. In particular, we discuss the quantification of ergodicity via concentration inequalities, and we illustrate that the latter in combi- nation with elliptic regularity theory leads to a quantification of the growth of the sublinear corrector and the homogenization error.
非对称椭圆有限差分方程随机均匀化修正器的矩界
影响因子：
1.9
作者：
Ben-Artzi J
通讯作者：
Ben-Artzi J