Bers和Finn关于孤立奇点可移性的定理在与一般线性增长问题有关的Euler-Lagrange方程中的推广
An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler-Lagrange equations related to general linear growth problems
摘要：
Bers和Finn的一个著名定理指出非参数极小曲面方程解的孤立奇点是可去除的。我们表明，这一结果仍然有效，如果面积泛函被替换为一般功能的线性增长依赖于梯度的模量。我们强调Serrin（[1]）事实上证明了在更一般的情况下，$(n-1)$维Hausdorff测度为零的集合上奇点的可移除性。我们的主要兴趣是推广比较原理，例如，在[2]的第10节中，没有特殊的几何结构的极小曲面。事实证明，广义悬链作为一个适当的工具来证明我们的结果。
英文摘要：
A famous theorem of Bers and Finn states that isolated singularities of solutions to the non-parametric minimal surface equation are removable. We show that this result remains valid, if the area functional is replaced by a general functional of linear growth depending on the modulus of the gradient. We emphasize that Serrin ([1]) in fact proved the removability of singularities on sets of $(n-1)$-dimensional Hausdorff measure zero in an even more general setting. Our main interest is to generalize the comparison principles as outlined, for instance, in Section 10 of [2] without having the particular geometric structure of minimal surfaces. It turns out that generalized catenoids serve as an appropriate tool for proving our results.
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