In a domain \(\Omega \subset {\mathbb {R}}^{n}\) whose boundary is smooth except on a set \({\mathcal {C}}\) of codimension (in \(\partial \Omega \)) k, the behavior of a nonparametric prescribed mean curvature hypersurface \(z=f\left( \mathbf{x}\right) \) in the vertical cylinder \(\Omega \times {\mathbb {R}}\) at a point \({\mathcal {O}}\in {\mathcal {C}}\) can be largely unknown when \(n\ge 3,\) depending on the type of boundary condition f satisfies. In a previous note, the authors considered an example in which \(n=3\) and \(k=2;\) that is, when \({\mathcal {C}}\) is a (nonconvex) conical point on \(\partial \Omega .\) Here, we consider prescribed mean curvature boundary value problems which are rotationally symmetric and investigate the behavior of variational solutions near a point \(P\in {\mathcal {C}}\) when \(n=3\) and \(k=1.\)

在一个域\（\ Omega \ subset {\ mathbb {R}} ^ {n} \）中，其边界是光滑的，除了在余维\\ {{mathcal {C}} \\}的集合中（在\（\ partial \ Omega \））k，在垂直圆柱体\（\ Omega \ times {\ mathbb {R}}中非参数规定平均曲率超曲面\（z = f \ left（\ mathbf {x} \ right）\）的行为\）在点\（{\ mathcal {ö}} \在{\ mathcal {C}} \）可以是很大程度上是未知的时\（N \ GE 3，\）取决于边界条件的类型˚F满足。在先前的注释中，作者考虑了一个示例，其中\（n = 3 \）和\（k = 2; \）即\（{\ mathcal {C}} \}是\（\ partial \ Omega。\）上的一个（非凸）圆锥点。在这里，我们考虑旋转对称的规定平均曲率边界值问题，并研究附近的变分解的行为。当\（n = 3 \）和\（k = 1。\）时的点\（P \在{\ mathcal {C}} \\）