论文标题
在广义高斯图上直接最小化坎汉姆 - 赫尔夫里奇的能量
Direct minimization of the Canham--Helfrich energy on generalized Gauss graphs
论文作者
论文摘要
证明了在广义高斯图的设置中的最小化物的最小化功能。作为第一步，通常在常规表面上定义的坎汉姆 - 赫尔夫里奇功能扩展到广义高斯图，然后在适当的条件下证明了较低的半连续性和紧凑性在弯曲常数的适当条件下，以确保施加性；最小化是通过变异的直接方法进行的。关于最小化器的规律性和功能的行为，如果缺乏强制性的评论。
The existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss graphs, then lower semicontinuity and compactness are proved under a suitable condition on the bending constants ensuring coerciveness; the minimization follows by the direct methods of the Calculus of Variations. Remarks on the regularity of minimizers and on the behavior of the functional in case there is lack of coerciveness are presented.
