论文标题
关于静电问题和新的$ \ mathbb {r}^3 $的新的特殊子域
On an electrostatic problem and a new class of exceptional subdomains of $\mathbb{R}^3$
论文作者
论文摘要
我们研究了非平凡的无界表面的存在$ s \ subset \ mathbb {r}^3 $与$ s $上的恒定电荷分布是静电平衡的属性，即产生的静电力是$ s $的每个点的表面。在有限的常规表面$ s $中，只有Reichel $ [23] $的结果（另请参见Mendez and Reichel $ [16] $）才能确认P. Gruber的猜想。在本文中，我们显示了非平凡的异常域的存在$ω\ subset \ mathbb {r}^3 $的边界$ s = \partialΩ$享受上述属性。
We study the existence of nontrivial unbounded surfaces $S\subset \mathbb{R}^3$ with the property that the constant charge distribution on $S$ is an electrostatic equilibrium, i.e. the resulting electrostatic force is normal to the surface at each point on $S$. Among bounded regular surfaces $S$, only the round sphere has this property by a result of Reichel $[23]$ (see also Mendez and Reichel $[16]$) confirming a conjecture of P. Gruber. In the present paper, we show the existence of nontrivial exceptional domains $Ω\subset \mathbb{R}^3$ whose boundaries $S=\partial Ω$ enjoy the above property.
