广义高斯图上Canham-Helfrich能量的直接最小化
Direct minimization of the Canham--Helfrich energy on generalized Gauss graphs
AI总结：
本文将Canham-Helfrich泛函扩展至广义高斯图，在弯曲常数满足强制性条件下利用变分法直接方法证明了极小值存在性，并讨论了正则性与缺乏强制性时的行为。
摘要：
本文证明了Canham-Helfrich泛函在广义高斯图设定下极小值的存在性。首先，将通常定义于正则曲面上的Canham-Helfrich泛函扩展至广义高斯图；随后，在确保强制性的弯曲常数适当条件下，证明了下半连续性与紧致性；极小化通过变分法的直接方法实现。此外，还讨论了极小值的正则性及缺乏强制性时泛函的行为。
英文摘要：
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.
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