Graph properties for nonlocal minimal surfaces
Graph properties for nonlocal minimal surfaces
复制标题
DOI：
10.1007/s00526-016-1020-9
复制
发表时间：
2015-06
影响因子：
2.1
通讯作者：
S. Dipierro;O. Savin;E. Valdinoci
中科院分区：
文献类型：
--
作者：
S. Dipierro;O. Savin;E. Valdinoci
本文证明了非局部极小曲面是柱面外的图，实际上是整个空间内的图。因此，在第三维，我们证明了图是光滑的。这些证明依赖于卷积技术和适当的积分估计，证明了与非局部平均曲率相关的欧拉-拉格朗日方程的点向有效性。
In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension 3, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler–Lagrange equation related to the nonlocal mean curvature.