论文标题
穿孔域中对Dirichlet问题的统一估计
Uniform Estimates for Dirichlet Problems in Perforated Domains
论文作者
论文摘要
本文研究了拉普拉斯方程在域中的差异问题，$ω_ {\ varepsilon，η} $带有小孔，其中$ \ varepsilon $代表了孔和$η$之间的最小距离的规模，而$η$之间的比例是holles和$ \ varepsilon $ \ varepsilon $。我们建立了$ w^{1，p} $估计，用于具有界定常数的解决方案，根据小参数$ \ varepsilon $和$η$明确。我们还表明，这些估计值是最佳或接近最佳的。
This paper studies the Dirichlet problem for Laplace's equation in a domain $Ω_{\varepsilon, η}$ perforated with small holes, where $\varepsilon$ represents the scale of the minimal distances between holes and $η$ the ratio between the scale of sizes of holes and $\varepsilon$. We establish $W^{1, p}$ estimates for solutions with bounding constants depending explicitly on the small parameters $\varepsilon$ and $η$. We also show that these estimates are either optimal or near optimal.
