O 'Hara纽结能量的离散化及其收敛性
A discretization of O'Hara's knot energy and its convergence
摘要：
在本文中，我们提出了一个离散版本的奥哈拉结能量定义在嵌入在欧几里得空间的多边形。证明了内接于O 'Hara能量有界的曲线的多边形的离散能量值收敛于其曲线的O' Hara能量值。并证明了离散能量在$Γ$ -收敛意义下收敛于O 'Hara能量.由于$Γ$ -收敛与泛函和离散泛函的极小化有关，我们需要研究离散能量的极小性。
英文摘要：
In this paper, we propose a discrete version of O'Hara's knot energy defined on polygons embedded in the Euclid space. It is shown that values of the discrete energy of polygons inscribing the curve which has bounded O'Hara's energy converge to the value of O'Hara's energy of its curve. Also, it is proved that the discrete energy converges to O'Hara's energy in the sense of $Γ$-convergence. Since $Γ$-convergence relates to minimizers of a functional and discrete functionals, we need to investigate the minimality of the discrete energy.
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