Neumann Problem in Domains with Outlets of Bounded Diameter
Neumann Problem in Domains with Outlets of Bounded Diameter
复制标题
具有有界直径出口的域中的诺依曼问题
DOI：
10.1023/a:1019736224759
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
G. Thäter
中科院分区：
文献类型：
--
作者：
G. Thäter
研究了具有拟圆柱形出口的域上拉普拉斯方程的Neumann问题。目的是收集和整理散布在文献中的已知结果，并填补仍然存在的理论空白。一方面应用Helmholtz分解，另一方面应用Riesz表示定理，得到了有限Dirichlet积分的Namley解。我们研究了非hilbert空间设置的推广，并收集了几种类型的Saint Venant估计。
We study the Neumann problem for the Laplace equation in domains having quasicylindrical outlets. The aim is to collect and sort known results spread over the literature and to fill in the gaps of the theory which still exist. Namley, solutions with finite Dirichlet integral are found applying on the one hand the Helmholtz decomposition and on the other hand the Riesz representation theorem. We investigate generalizations for the non-Hilbert space setting and collect several types of Saint Venant estimates.