论文标题
椭圆化均质化和特征函数的估计值迅速振荡电势
Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials
论文作者
论文摘要
在本文中，对于一个二阶椭圆方程的家族，具有迅速振荡的周期性系数和迅速振荡的周期性潜力，我们对$ H^1 $收敛速率以及Dirichlet Eigenvalues及其dirichlet eigenvalues and Bounds and Bounters感兴趣。 $ h^1 $融合率依赖于dirichlet校正器和一阶校正器来振荡电势。而且，限制结果依赖于$ o（\ varepsilon）$ h^1 $的$ o（\ varepsilon）$估计。
In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients and rapidly oscillating periodic potentials, we are interested in the $H^1$ convergence rates and the Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The $H^1$ convergence rates rely on the Dirichlet correctors and the first-order corrector for the oscillating potentials. And the bound results rely on an $O(\varepsilon)$ estimate in $H^1$ for solutions with Dirichlet condition.
