On uniform estimates for Laplace equation in balls with small holes
On uniform estimates for Laplace equation in balls with small holes
复制标题
小孔球拉普拉斯方程的统一估计
DOI：
10.1007/s00526-016-1055-y
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Yong
中科院分区：
文献类型：
--
作者：
Yong
本文考虑了三维拉普拉斯方程在带收缩孔的单位球上的Dirichlet问题。这个问题通常是由均匀化问题在域穿孔与微小的孔。我们给出了一个几乎完整的描述有关的uniformestimates：对于anythere举行uniformestimates;对于anyor，有反例表明uniformestimates不成立。所得结果可以推广到高维空间。
In this paper, we consider the Dirichlet problem of the three-dimensional Laplace equation in the unit ball with a shrinking hole. The problem typically arises from homogenization problems in domains perforated with tiny holes. We give an almost complete description concerning the uniformestimates: for anythere hold the uniformestimates; for anyor, there are counterexamples indicating that the uniformestimates do not hold. The results can be generalized to higher dimensions.