具有自由边界的Willmore曲面的反射
Reflection of Willmore surfaces with free boundaries
AI总结：
本文研究三维空间中带边界约束的Willmore曲面临界点，针对两种自由边界情形推导弱形式条件，并利用反射方法证明正则性。
摘要：
我们研究在边界约束下作为Willmore泛函临界点的浸入$\u211d^3$曲面。考虑两种情形：曲面沿边界与平面正交相交，以及边界包含于一条直线。在两种情形下，我们推导所得自由边界条件的弱形式，并通过反射证明正则性。
英文摘要：
We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
