论文标题
形状分析性和奇异扰动的层潜在操作员
Shape analyticity and singular perturbations for layer potential operators
论文作者
论文摘要
我们研究了规则和奇异域扰动对拉普拉斯方程层潜在操作员的影响。首先，我们考虑参考集合$ \partialΩ$的DiffeMormorthic Image $ ϕ（\partialΩ）$支持的图层电势，并且我们给出了一些对映射$ ϕ $的依赖性的真实分析结果。然后，我们引入了带有大小$ε$的小孔的穿孔域$ω（ε）$，并计算功率系列扩展，该扩展描述了$ \partialΩ（ε）$上的层势时，当参数$ε$近似值近似值$ε= 0 $。
We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image $ϕ(\partialΩ)$ of a reference set $\partialΩ$ and we present some real analyticity results for the dependence upon the map $ϕ$. Then we introduce a perforated domain $Ω(ε)$ with a small hole of size $ε$ and we compute power series expansions that describe the layer potentials on $\partialΩ(ε)$ when the parameter $ε$ approximates the degenerate value $ε=0$.
