无径向限制的毛细曲面
A Capillary Surface with No Radial Limits
摘要：
1996年，Kirk Lancaster和David Siegel研究了毛细管和其他具有接触角边界数据的规定平均曲率问题的解域边界角处的径向极限的存在性和行为。在定理3中，它们提供了单位盘$D$中的毛细管表面的示例，该单位盘在$(0,0)\in\partial D.$处没有径向限制。在它们的示例中，接触角（$γ$）这里，我们考虑在$π.$处具有凸角的域$Ω$，并在$Ω\times\mathbb{R}$中找到毛细表面$z=f(x,y)$，其在$(0,0)\in\partialΩ$处没有径向限制，使得$γ$远离$0$和$π.$
英文摘要：
In 1996, Kirk Lancaster and David Siegel investigated the existence and behavior of radial limits at a corner of the boundary of the domain of solutions of capillary and other prescribed mean curvature problems with contact angle boundary data. In Theorem 3, they provide an example of a capillary surface in a unit disk $D$ which has no radial limits at $(0,0)\in\partial D.$ In their example, the contact angle ($γ$) cannot be bounded away from zero and $π.$ Here we consider a domain $Ω$ with a convex corner at $(0,0)$ and find a capillary surface $z=f(x,y)$ in $Ω\times\mathbb{R}$ which has no radial limits at $(0,0)\in\partialΩ$ such that $γ$ is bounded away from $0$ and $π.$
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