论文标题
最佳$ c^{1，\ frac {1} {2}} $ - $ h $ -surfaces具有免费边界的规律性
Optimal $C^{1,\frac{1}{2}}$-regularity of $H$-surfaces with a free boundary
论文作者
论文摘要
我们证明，在二维$ c^2 $ -manifold上具有自由边界的规定平均曲率表面（$ h $ -SURFACE）属于$ C^{1，\ frac {1} {2} {2}}} $，只要它是一个持续的边界。我们允许$ h $ -surface符合歧管，并具有歧管本身具有边界。根据Hildebrandt和Nitsche的示例，我们的结果是最佳的。
We prove that a surface of prescribed mean curvature ($H$-surface) with free boundary on a two-dimensional $C^2$-manifold belongs to $C^{1,\frac{1}{2}}$ up to that the boundary, provided it is a-priori continuous. We allow the $H$-surface to meet the manifold non-perpendicularly and the manifold itself to have a boundary. Our result is optimal according to an example of Hildebrandt and Nitsche.
