论文标题
Bernstein型定理的稳定性最小表面方程
Stability of Bernstein type theorem for the minimal surface equation
论文作者
论文摘要
令$ω\ subsetneq \ mathbf {r}^n \，（n \ geq 2）$为无界的凸域。我们研究了$ω$中的最小表面方程，并以线性函数和$ \ mathbf {r}^n $中有限的统一连续函数给出的边界值。如果$ω$不是半空间，我们证明解决方案是唯一的。如果$ω$是一个半空间，我们证明所有解决方案的图形构成了$ω\ times \ mathbf {r} $的叶面。这可以看作是Edelen-Wang的Bernstein Type定理\ Cite {eW2021}中的稳定性定理。我们还为$ω$建立了最小表面方程的比较原理。
Let $ Ω\subsetneq \mathbf{R}^n\,(n\geq 2)$ be an unbounded convex domain. We study the minimal surface equation in $Ω$ with boundary value given by the sum of a linear function and a bounded uniformly continuous function in $ \mathbf{R}^n$. If $ Ω$ is not a half space, we prove that the solution is unique. If $ Ω$ is a half space, we prove that graphs of all solutions form a foliation of $Ω\times\mathbf{R}$. This can be viewed as a stability type theorem for Edelen-Wang's Bernstein type theorem in \cite{EW2021}. We also establish a comparison principle for the minimal surface equation in $Ω$.
