论文标题
椭圆系统的均质化理论，具有较低的术语的尺寸二
Homogenization Theory of Elliptic System with Lower Order Terms for Dimension Two
论文作者
论文摘要
在本文中，我们考虑了通用椭圆系统$$的均质化问题\ Mathcal {l} _ {\ varepsilon} = - \ protatorName {div}（a（x/\ varepsilon）\ nabla+v（x/\ varepsilon））+b（x/\ varepsilon）确切地说，我们将建立$ w^{1，p} $估计，Hölder估计，Lipschitz估计值和$ l^p $收敛结果，用于$ \ Mathcal {l} _ {\ varepsilon} $，并带有尺寸二。运算符$ \ MATHCAL {l} _ {\ VAREPSILON} $已由Qiang Xu研究了dimension $ d \ geq 3 $ in \ cite {xu1，xu2}，并且case $ d = 2 $剩余。作为副产品，我们将以$ \ Mathcal {l} _ {\ varepsilon} $构建绿色功能，并使用$ d = 2 $及其收敛速度。
In this paper, we consider the homogenization problem for generalized elliptic systems $$ \mathcal{L}_{\varepsilon}=-\operatorname{div}(A(x/\varepsilon)\nabla+V(x/\varepsilon))+B(x/\varepsilon)\nabla+c(x/\varepsilon)+λI $$ with dimension two. Precisely, we will establish the $ W^{1,p} $ estimates, Hölder estimates, Lipschitz estimates and $ L^p $ convergence results for $ \mathcal{L}_{\varepsilon} $ with dimension two. The operator $ \mathcal{L}_{\varepsilon} $ has been studied by Qiang Xu with dimension $ d\geq 3 $ in \cite{Xu1,Xu2} and the case $ d=2 $ is remained unsolved. As a byproduct, we will construct the Green functions for $ \mathcal{L}_{\varepsilon} $ with $ d=2 $ and their convergence rates.
