论文标题
泊松和斯托克斯方程在整个空间中的均匀化
Homogenization of Poisson and Stokes equations in the whole space
论文作者
论文摘要
我们考虑泊松的均匀化和整个空间中的Stokes方程，并用定期分布的小孔穿孔。遵循[24、4、1、2]的经典结果，对有限域中的周期性均质化已得到充分了解。在本文中，我们表明，这些经典的均质化导致有限的域可以扩展到整个空间$ {\ mathbb r}^d $。我们的结果涵盖了所有三个案例，对应于不同尺寸的孔，并覆盖所有$ d \ geq 2 $。
We consider the homogenization of the Poisson and the Stokes equations in the whole space perforated with periodically distributed small holes. The periodic homogenization in bounded domains is well understood, following the classical results in [24, 4, 1, 2]. In this paper, we show that these classical homogenization results in a bounded domain can be extended to the whole space ${\mathbb R}^d$. Our results cover all three cases corresponding to different sizes of holes and cover all $d\geq 2$.
