论文标题
最小化具有弹性边界的弹性表面能的配置
Minimizing Configurations for Elastic Surface Energies with Elastic Boundaries
论文作者
论文摘要
我们研究了表面能的临界表面，其中包含平方的$ l^2 $规范的平均曲率$ h $和自发曲率$ C_O $的差异，并与边界曲线的弹性能相结合。我们使用$ h \ equiv -c_o $研究了平衡的存在。 当$ c_o \ ge 0 $时，我们表征了那些对拓扑结构有限的能量有限的情况，并且在其存在的情况下，我们发现了最小化器。还给出了拓扑盘的结果。
We study critical surfaces for a surface energy which contains the squared $L^2$ norm of the difference of the mean curvature $H$ and the spontaneous curvature $c_o$, coupled to the elastic energy of the boundary curve. We investigate the existence of equilibria with $H\equiv -c_o$. When $c_o \ge 0$ we characterize those cases where the infimum of this energy is finite for topological annuli and we find the minimizer in the cases that it exists. Results for topological discs are also given.
