论文标题
与部分自由边界的非参数高原问题
A non-parametric Plateau problem with partial free boundary
论文作者
论文摘要
我们考虑在非参数环境中的Codimension $ 1 $中的平稳问题。仅在边界$ \ partialω$的一部分的dirichlet边界基准中给出了一个有界凸域$ω\ subset \ mathbb {r}^2 $的部分$ \ partialω$。如果未开处方Dirichlet基准，我们允许与水平平面进行免费接触。我们显示了解决方案的存在，并证明了相应最小表面的规律性。最后，我们将这些解决方案与Meeks和Yau的经典最小表面进行了比较，并表明当将Dirichlet边界数据分配给最多$ 2 $ discoint Arcs时，它们是等效的。
We consider a Plateau problem in codimension $1$ in the non-parametric setting. A Dirichlet boundary datum is given only on part of the boundary $\partial Ω$ of a bounded convex domain $Ω\subset\mathbb{R}^2$. Where the Dirichlet datum is not prescribed, we allow a free contact with the horizontal plane. We show existence of a solution, and prove regularity for the corresponding minimal surface. Finally we compare these solutions with the classical minimal surfaces of Meeks and Yau, and show that they are equivalent when the Dirichlet boundary datum is assigned in at most $2$ disjoint arcs of $\partial Ω$.
