Convergence rates for elliptic reiterated homogenization problems
Jie Zhao · Communications on Pure & Applied Analysis · 2013
In this paper, we study the convergence rates for the reiteratedhomogenization for equations of the form$-div(A(\frac{x}{\varepsilon},\frac{x}{\varepsilon^{2}}) abla u_{\varepsilon})=f(x)$. As a consequence,we obtain the convergence rates in $L^{p}$ for solutions with Dirichlet boundary conditionby a method based on the representation of elliptic equation solution by Green function.Meanwhile, the growth rate of Green function is found.